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Stefan Ivkovic

Publications and source records attributed to Stefan Ivkovic.

At least 19 recordsLinked to original sources
arXiv2026

On Topological Numerical Transitivity, C*-Transitivity and generalizations

Motivated by the concept of numerical hypercyclicity, in this paper, we introduce three new notions in linear dynamics: topological numerical transitivity, generalized numerical transitivity, C*-transitivity. The first notion is defined for operators on general Banach spaces, whereas the latter two are formulated in the setting of operators on Banach algebras. The concept of C*-transitivity is also applicable to operators on the space of Hilbert-Schmidt operators. We prove that these new notions are mutually different, and we also show that they differ from the standard notions in dynamics. In particular, while topological numerical transitivity implies numerical hypercyclicity, as we argue in the paper, we provide examples of numerically hypercyclic and strongly numerically hypercyclic operators that are not topologically numerically transitive. Also, we construct nonsupercyclic C* transitive and generalized numerically transitive operators on the C*-algebra of compact operators on a separable Hilbert space, as well as C*-transitive nonsupercyclic operators on the standard Hilbert C*-module. In addition, we study diagonal operators on finite-dimensional and separable Hilbert spaces, and we obtain complete characterizations of both numerical hypercyclicity and topological numerical transitivity in terms of coefficient-simplex criteria. Further, we provide some sufficient conditions for diagonal operators on the standard Hilbert C*-module to be C*-transitive. All these results are illustrated with concrete examples. At the end of the paper, we compare topological numerical transitivity and C*-transitivity with numerous standard notions in linear dynamics, and we prove that topological numerical transitivity and C*-transitivity genuinely differ from all these standard concepts in dynamics.

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arXiv2026

Spectral Fredholm Theory and Transitivity in Banach bimodules

In this paper, we extend Fredholm theory in von Neumann algebras established by Breuer to spectral Fredholm theory. We consider 2 by 2 upper triangular operator matrices with coefficients in a von Neumann algebra and give the relationship between the generalized essential spectra in the sense of Breuer of such matrices and of their diagonal entries. Next, we prove that if a generalized Fredholm operator in the sense of Breuer has 0 as an isolated point of its spectrum, then the corresponding spectral projection is finite. Finally, we define the generalized B-Fredholm operator in a von Neumann algebra as a generalization in the sense of Breuer of the classical B-Fredholm operators on Hilbert and Banach spaces. We provide sufficient conditions under which a sum of a generalized B-Fredholm operator and a finite operator in a von Neumann algebra is again a generalized B-Fredholm operator. Finally, motivated by the connections between supercyclicity and semi-Fredholm theory, in the last section of the paper, we characterize disjoint supercyclic and disjoint Furstenberg semi-transitive operators on a large class of Banach bimodules.

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arXiv2026

Periodicity in Banach algebras

In this paper, we consider operators that are compositions of an isometric isomorphism and a left multiplier on a Banach algebra, and we provide necessary and sufficient conditions for these operators to have a dense set of periodic elements. As an application of this result, we characterize generalized weighted shifts with a dense set of periodic elements on the standard Hilbert module over C*-algebra of compact operators on a separable Hilbert space. As another application, we characterize generalized weighted shifts with a dense set of periodic elements on the standard Hilbert module over commutative non-unital C*-algebra.

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arXiv2026

Pseudo-Riesz sequences in Hilbert C*-modules

Motivated by the concept of pseudo-Riesz sequences and pseudo- Riesz bases in Hilbert spaces, recently introduced by Biswas and Mitkovski, in this paper, we study pseudo-Riesz sequences and pseudo-Riesz bases in the standard Hilbert module over a unital C*-algebra. We prove that a Bessel sequence in the standard Hilbert C*-module is a pseudo-Riesz sequence if and only if the associated synthesis operator is upper semi-C*-Fredholm. Moreover, we introduce a new notion of pseudo-Riesz-Weyl sequences in Hilbert C*-modules and we prove that a Bessel sequence in the standard Hilbert C*-module is pseudo-Riesz-Weyl if and only if the associated synthesis operator is upper semi-C*-Weyl. We apply the obtained results in the study of perturbations of Bessel sequences in Hilbert C*-modules.

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arXiv2026

Disjoint F-semi-transitivity in Banach algebras

In this paper, we consider the concept of disjoint Furstenberg-semi-transitivity for operators that are a composition of an isometric isomorphism and a left multiplier on a normed algebra. Thus, we characterize disjoint F-semi-transitive and disjoint supercyclic such operators on a large class of non-unital normed algebras. It turns out that generalized weighted bilateral shifts on the standard Hilbert C*-module are just a special case of our theory. Generalized weighted composition operators on the normed algebra of operator-valued continuous functions vanishing at infinity on a locally compact, non-compact Hausdorff space are another special case of our theory. Next, we characterize disjoint F-semi-transitive and disjoint supercyclic weighted composition operators on a large class of weighted solid Banach function spaces and apply our results to the case of translations on weighted Morrey spaces. We illustrate all the results in this paper with concrete examples.

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arXiv2026

Dynamics on weighted solid Banach function spaces

The dynamics of weighted translation operators on Lebesgue spaces, Orlicz spaces, and in general on solid Banach function spaces have been studied in numerous papers. Recently, the dynamics of weighted translations on weighted Orlicz spaces have also been studied by Chen and others. The main idea of this paper is to obtain a generalization of these results to the case of general weighted solid Banach function spaces. More precisely, in this paper, we characterize disjoint topologically transitive weighted composition operators on weighted solid Banach function spaces. This approach has applications in the dynamics of weighted translations on weighted Morrey spaces.

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arXiv2026

Cauchy-Schwarz inequalities for maps in noncommutative Lp-spaces

In this paper, a generalized Cauchy-Schwarz inequality for positive sesquilinear maps with values in noncommutative Lp-spaces for p > 1 are obtained. Bound estimates for their real and imaginary parts are also provided, and, as an application, a generalization of the uncertainty relation in the context of noncommutative L2-spaces are given. Next, a Cauchy-Schwarz inequality for positive sesquilinear maps with values in the space of bounded linear operators from a von Neumann algebra into a C*-algebra equipped with the numerical radius norm is proved. In the same spirit, a new norm on a noncommutative L2-space, which generalizes the classical numerical radius norm of bounded linear operators on a Hilbert space, is proposed, and a Cauchy-Schwarz inequality for positive sesquilinear maps with values in the space of bounded linear operators from a von-Neumann algebra into the noncommutative L2-space equipped with this new norm is proved. These results are used to get representations of general positive linear maps with values into a non-commutative Lp-space and into certain operator spaces in several different situations. Some concrete examples are also given.

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arXiv2025

Porosity and supercyclic operators on solid Banach function spaces

In this paper, we characterize supercyclic weighted composition operators on a large class of solid Banach function spaces, in particular on Lebesgue, Orlicz and Morrey spaces. Also, we characterize supercyclic weighted composition operators on certain Segal algebras of functions and nonunital commutative C*-algebras. Moreover, we introduce the concept of Cesáro hyper-transitivity and we characterize Cesáro hyper-transitive weighted composition operators on all these spaces. We illustrate our results with concrete examples and we give in addition an example of a hypercyclic weighted composition operator which is not Cesáro hyper-transitive. Next, we introduce a class of non-porous subsets of the space of continuous functions vanishing at infinity on the real line. As an application, we consider weighted composition operator on this space and we give sufficient conditions that induce that the set of non-hypercyclic vectors for this operator is non-porous.

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arXiv2025

Luh hypercyclic vector for composition operator

In this paper, we deal with the construction of holomorphic functions on a simply connected domain satisfying that all its derivatives and antiderivatives under a composition operator have a dense orbit. Such functions will be called Luh hypercyclic vectors for the respective composition operator. We show that there is a dense linear manifold of Luh hypercyclic vectors. Moreover, we study the dynamics of cosine operator function generated by weighted composition operators on solid Banach function spaces, in particular on Orlicz and Morrey spaces, and we give sufficient conditions for supercyclicity of such cosine operator functions in terms of the corresponding weight function. Also, we give concrete examples of weighted translations satisfying these sufficient conditions.

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arXiv2025

Dynamics of operators on the space of Radon measures

In this paper, we study the dynamics of the adjoint of a weighted composition operator and we give necessary and sufficient conditions for this adjoint operator to be topologically hyper-transitive on the space of Radon measures on a locally compact Hausdorff space. Moreover, we provide sufficient conditions for this operator to be chaotic and we give concrete examples. Next, we consider the real Banach space of signed Radon measures and we give in this context the sufficient conditions for the convergence of Markov chains induced by the adjoint of an integral operator. Also, we illustrate this result with a concrete example. In addition, we obtain some structural results regarding the space of Radon measures. We characterize a class of cones whose complement is spaceable in the space of Radon measures.

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arXiv2025

Banach bimodule-valued positive maps: Inequalities and induced representations

In this paper, we consider representations induced by general positive and completely positive sesquilinear maps with values in ordered Banach bimodules, such as the space of trace-class operators and the spaces of bounded linear operators from a von Neumann algebra into the dual of another von Neumann algebra. Also, we deduce some new inequalities for these maps.

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arXiv2024

On representations and topological aspects of positive maps on non-unital quasi *-algebras

In this paper, we provide a representation of a certain class of C*-valued positive sesquilinear and linear maps on non-unital quasi *-algebras. Also, we illustrate our results on the concrete examples of non-unital Banach quasi *-algebras, such as the standard Hilbert module over a commutative C*-algebra, Schatten p-ideals, and noncommutative L2 spaces induced by a semifinite, nonfinite trace. As a consequence of our results, we obtain a representation of all bounded positive linear C*-valued maps on non-unital C*-algebras. We also deduce some norm inequalities for these maps. Finally, we consider a noncommutative L2 space equipped with the topology generated by a positive sesquilinear form and we construct a topologically transitive operator on this space.

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arXiv2023

Disjoint linear dynamical properties of elementary operators

We characterize disjoint hypercyclic sequences of wedge operators. Also, we give some sufficient conditions for a sequence of the dual wedge operators to be disjoint topologically transitive. Finally, we give some concrete examples and applications.

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arXiv2023

On New Approach to semi-Fredholm theory in unital C*-algebras

Axiomatic Fredholm theory in unital C*-algebras was established by Keckic and Lazovic in [15]. Following the purely algebraic approach by Keckic and Lazovic, in [14] we extended further this theory to axiomatic semi-Fredholm and semi-Weyl theory in unital C*-algebras. However, recently, in [11] we developed another approach to axiomatic Fredholm theory in unital C*-algebras which is based on the theory of Hilbert modules and which is equivalent to the algebraic approach by Keckic and Lazovic. In this paper, we extend further this new Hilbert-module approach from Fredholm theory to semi-Fredholm and semi-Weyl theory in unital C*-algebras. Hence, we provide a new proof of the results in [14].

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arXiv2023

On New Approach to Fredholm theory in unital C*-algebras

Motivated by the Fredholm theory on the standard Hilbert module over an unital C*-algebra introduced by Mishchenko and Fomenko, we provide a new approach to axiomatic Fredholm theory in unital C*-algebras established by Keckic and Lazovic in [28]. Our approach is equivalent to the approach introduced by Keckic and Lazovic, however, we provide new proofs which are motivated by the proofs given by Mishchenko and Fomenko.

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arXiv2023

Hypercyclic Generalized Shift Operators

In this paper, we study the linear dynamical properties of shift operators on some classes of Segal algebras. Moreover, we characterize hypercyclic generalized bilateral shift operators on the standard Hilbert module.

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arXiv2023

Semi-Fredholm theory in C*-algebras

Keckic and Lazovic introduced an axiomatic approach to Fredholm theory by considering Fredholm-type elements in an unital C*-algebra as a generalization of C*-Fredholm operators on the standard Hilbert C*-module introduced by Mishchenko and Fomenko and of Fredholm operators on a properly infinite von Neumann algebra introduced by Breuer. In this paper, we establish the semi-Fredholm theory in unital C*-algebras as a continuation of the approach by Keckic and Lazovic. We introduce the notion of semi-Fredholm-type elements and semi-Weyl-type elements. We prove that the difference between the set of semi-Fredholm elements and the set of semi-Weyl elements is open in the norm topology, that the set of semi-Weyl elements is invariant under perturbations by finite type elements, and several other results generalizing their classical counterparts. Also, we illustrate applications of our results to the special case of properly infinite von Neumann algebras and we obtain a generalization of the punctured neighborhood theorem in this setting.

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