On collectively almost (limitedly, order) L-weakly compact sets of operators
We prove collective versions of semi-duality theorems for sets of almost (limitedly, order) L-weakly compact operators.
math.FA↗
arXiv subjects
Svetlana Gorokhova
Publications and source records attributed to Svetlana Gorokhova.
On automatic continuity of operators from ordered to topological vector spaces
We study continuity and boundedness of order-to-topology bounded and order-to topology continuous operators from ordered to topological vector spaces. Several results on automatic continuity of operators from ordered Frechet spaces to topological vector spaces are included. Levi and Lebesgue operators especially are investigated.
math.FA↗
On ortho and disjointly compact operators acting to Frechet spaces
We study compactness along orthonormal (disjoint bounded) sequences for operators from Hilbert spaces (Banach lattices) to Frechet spaces.
math.FA↗
Free uniformly complete vector lattices
We define a free uniformly complete vector lattice over a set of generators and give its concrete representation as a space of continuous positively homogeneous functions.
math.FA↗
On limited and almost limited operators between Banach lattices
We study (almost) limited operators in Banach lattices and their relations to L-weakly compact, semi-compact, and Dunford-Pettis operators. Several further related topics are investigated.
math.FA↗
Collective order boundedness of sets of operators between ordered vector spaces
It is proved that: each collectively order continuous set of operators from an Archimedean OVS with a generating cone to an OVS is collectively order bounded; and each collectively order to norm bounded set of operators from an ordered Banach space with a closed generating cone to a normed space is norm bounded. Several applications to commutative operator semigroups on ordered vector spaces are given.
math.FA↗
Relatively uniformly continuous semigroups on ordered vector spaces
We study relatively uniformly continuous operator semigroups on ordered vector spaces and extend several recent results obtained by M. Kramar Fijavz, M. Kandic, M. Kaplin, and J. Gluck in the vector lattice setting to ordered vector spaces with generating cones.
math.FA↗
d-Operators in Banach Lattices
We study operators carrying disjoint bounded subsets of a Banach lattice into compact, weakly compact, and limited subsets of a Banach space. Surprisingly, these operators behave differently with classical compact, weakly compact, and limited operators. We introduce and investigate d-Andrews operators which carry disjoint bounded sets onto Dunford--Pettis sets.
math.FA↗
On compact (limited) operators between Hilbert and Banach spaces
We give orthonormal characterizations of collectively compact (limited) sets of linear operators from a Hilbert space to a Banach space.
math.FA↗
On aL(M)wc and oL(M)wc operators between Banach lattices
We study almost L(M) weakly compact and order L(M) weakly compact operators in Banach spaces. Several further topics related to these operators are investigated.
math.FA↗
Duality and Norm Completeness in the Classes of Limitedly--Lwc and Dunford--Pettis--Lwc Operators
We investigate the duality and norm completeness in the classes of limitedly--L-weakly compact and Dunford--Pettis--L-weakly compact and operators from Banach spaces to Banach lattices.
math.FA↗
Limitedly L-weakly compact operators
We introduce new class of limitedly L-weakly compact operators from a Banach space to a Banach lattice. This class is a proper subclass of the Bourgain-Diestel operators and it contains properly the class of L-weakly compact operators. We give its efficient characterization in term of sequences, investigate the domination problem, and study the completeness of this class of operators.
math.FA↗
Generalizations of L- and M-weakly compact operators
L- and M-weakly compact operators were introduced by Meyer-Nieberg in the beginning of seventies in attempts of a diversification of the concept of weakly compact operators via imposing Banach lattice structure on the range or on the domain of operators. We investigate regularity and algebraic properties of various generalizations of L- and M-weakly compact operators from a unified point of view via using regularly P-operators.
math.FA↗
Enveloping norms on the spaces of regularly P-operators in Banach lattices
We introduce and study the enveloping norms of regularly P-operators between Banach lattices E and F, where P is a subspace of the space L(E,F) of continuous operators from E to F. We prove that if P is closed in L(E,F) in the operator norm then the regularly P-operators forms a Banach space under the enveloping norm. Conditions providing that regularly P-operators forms a Banach lattice under the enveloping norm are given.
math.FA↗
Regularly limited, Grothendieck, and Dunford--Pettis operators
We introduce and study the enveloping norms of regularly P-operators, where P is an "almost" version of limited, Grothendieck, and of Dunford--Pettis operators in Banach lattices. Several further topics related to these operators are also discussed.
math.FA↗
Operators Affiliated to Banach Lattice Properties and the Enveloping Norms
Several recent papers were devoted to various modifications of limited, Grothendieck, and Dunford--Pettis operators, etc., through involving the Banach lattice structure. In the present paper, it is shown that many of these operators appear as operators affiliated to well known properties of Banach lattices, like the disjoint (dual) Schur property, the disjoint Grothendieck property, the property (d), and the sequential w*-continuity of the lattice operations. It is proved that the spaces consisting of regularly versions of the above operators are all Banach spaces. The domination problem for such operators is investigated.
math.FA↗
The $oτ$-continuous, Lebesgue, KB, and Levi operators between vector lattices and topological vector spaces
We investigate the $oτ$-continuous/bounded/compact and Lebesgue operators from vector lattices to topological vector spaces; the KB operators between locally solid lattices and topological vector spaces; and the Levi operators from locally solid lattices to vector lattices. The main idea of operator versions of notions related to vector lattices lies in redistributing topological and order properties of a topological vector lattice between the domain and range of an operator under investigation. Domination properties for these classes of operators are studied.
math.FA↗
Multiplicative order compact operators between vector lattices and $l$-algebras
In the present paper, we introduce and investigate the multiplicative order compact operators from vector lattices to $l$-algebras. A linear operator $T$ from a vector lattice $X$ to an $l$-algebra $E$ is said to be $\mathbb{omo}$-compact if every order bounded net $x_α$ in $X$ possesses a subnet $x_{α_β}$ such that $Tx_{α_β}\moc y$ for some $y\in E$. We also introduce and study $\mathbb{omo}$-$M$- and $\mathbb{omo}$-$L$-weakly compact operators from vector lattices to $l$-algebras.
math.FA↗