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Full-Text Articles in Physical Sciences and Mathematics
Operators Affiliated To Banach Lattice Properties And Their Enveloping Norms, Eduard Emelyanov, Svetlana Gorokhova
Operators Affiliated To Banach Lattice Properties And Their Enveloping Norms, Eduard Emelyanov, Svetlana Gorokhova
Turkish Journal of Mathematics
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), the sequential w$^\ast$-continuity of the lattice operations, etc. We also introduce new classes of operators such as the s-GPP-operators, s-BDP-operators, and bi-sP-operators. It is proved that the spaces consisting of regular versions of the above-mentioned operators are all the Banach spaces. The domination problem …
The Class Of Demi Kb-Operators On Banach Lattices, Hedi Benkhaled, Aref Jeribi
The Class Of Demi Kb-Operators On Banach Lattices, Hedi Benkhaled, Aref Jeribi
Turkish Journal of Mathematics
In this paper, we introduce and study the new concept of demi KB-operators. Let $E$ be a Banach lattice. An operator $T: E\longrightarrow E$ is said to be a demi KB-operator if, for every positive increasing sequence $\{x_{n}\}$ in the closed unit ball $\mathcal{B}_{E}$ of $E$ such that $\{x_{n}-Tx_{n}\}$ is norm convergent to $x\in E$, there is a norm convergent subsequence of $\{x_{n}\}$. If the latter sequence has a weakly convergent subsequence then $T$ is called a weak demi KB-operator. We also investigate the relationship of these classes of operators with classical notions of operators, such as b-weakly demicompact operators …