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Safak Alpay

Publications and source records attributed to Safak Alpay.

11 recordsLinked to original sources
arXiv2023

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↗
arXiv2023

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↗
arXiv2022

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↗
arXiv2022

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↗
arXiv2022

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↗
arXiv2021

b-Property of sublattices in vector lattices

We study $b$-property of a sublattice (or an order ideal) $F$ of a vector lattice $E$. In particular, $b$-property of $E$ in $E^δ$, the Dedekind completion of $E$, $b$-property of $E$ in $E^u$, the universal completion of $E$, and $b$-property of $E$ in $\hat{E}(\hatτ)$, the completion of $E$.

math.FA↗
arXiv2020

Bibounded uo-convergence and b-property in vector lattices

We define bidual bounded $uo$-convergence in vector lattices and investigate relations between this convergence and $b$-property. We prove that for a regular Riesz dual system $\langle X,X^{\sim}\rangle$, $X$ has $b$-property if and only if the order convergence in $X$ agrees with the order convergence in $X^{\sim\sim}$.

math.FA↗