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Cristian Ivanescu

Publications and source records attributed to Cristian Ivanescu.

6 recordsLinked to original sources
arXiv2026

On bounded module functionals and operators on Hilbert C*-modules without biorthogonally complemented kernels

We investigate the structural reasons behind the existence and non-existence of bounded module functionals and bounded module operators on Hilbert C*-modules whose kernels are not orthogonally complemented. The key motivating example was introduced by J. Kaad and M. Skeide in their 2023 paper. Building on their ideas and related developments, we obtain a structural characterization of this class of examples in a more abstract theoretical framework. We also study non-adjointable bounded module operators associated with such module functionals, together with the properties of the corresponding operator algebras and operator spaces. Our results provide a deeper understanding of phenomena beyond the adjointable setting, place several existing partial results into a unified framework, and show how large families of further examples can be constructed systematically.

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arXiv2023

Villadsen algebras

C*-algebras are rings, sometimes nonunital, obeying certain axioms that ensure a very well-behaved representation theory upon Hilbert space. Moreover, there are some well-known features of the representation theory leading to subtle questions about norms on tensor products of C*-algebras, and thus to the subclass of nuclear C*-algebras. The question whether all separable nuclear C*-algebras satisfy the Universal Coefficient Theorem (UCT) remains one of the most important open problems in the structure and classification theory of such algebras. One of the most promising ways to test the UCT conjecture depends on finding C*-algebras that behave as idempotents under the tensor product, and satisfy certain additional properties. Briefly put, it has been shown that if there exists a simple, separable, and nuclear C*-algebra that is an idempotent under the tensor product, satisfies a certain technical property, and is not one of the already known such elements $\left\{ O_\infty, O_2, \UHF , J, Z, \C, \compact \right\}$ then the UCT fails. Although we do not disprove the UCT in this publication, we do find new idempotents in the class of Villadsen algebras.

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arXiv2016

The Cuntz semigroup of the tensor product C*-algebras

We calculate the Cuntz semigroup of the tensor product A with A. We restrict our attention to C*-algebras A which are unital, simple, nuclear, stably finite, have stable rank one, absorbs the Jiang-Su algebra tensorially and satisfy the UCT.

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arXiv2007

The classification ofseparable simple C*-algebras which are inductive limits of continuous-trace C*-algebraswith spectrum homeomorphic to the closed interval [0,1]

A classification is given of certain separable nuclear C*-algebras not necessarily of real rank zero, namely, the class of separable simple C*-algebras which are inductive limits of continuous-trace C*-algebras whose building blocks have spectrum homeomorphic to the closed interval [0,1], or to a disjoint union of copies of this space. Also, the range of the invariant is calculated.

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