Grothendieck Banach lattices and classes of 𝒑− convergent operators

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Ardakani Halimeh; Salimi Manijeh

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Journal Paper

Paper Information

Journal: Mathematical Researches Year:2024 | Volume:10 | Issue:3 Page(s): 1-17

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Information Journal Paper

Title

Grothendieck Banach lattices and classes of 𝒑− convergent operators

Author(s)

Ardakani Halimeh | Salimi Manijeh | Issue Writer Certificate

Keywords

L-set

weakly p-summable sequence

p-convergent operator

p-Schur property

Banach lattice.

Abstract

Recently, the concept of 𝐿−limited subsets of order 𝑝 (1≤𝑝<∞) in dual Banach spaces and limited p-convergent operators are introduced. The paper is devoted to some results of almost 𝐿−limited subsets of order p in dual Banach lattice. and disjoint limited 𝑝−convergent operators. In particular, we derive the following result: Banach lattice. with the property that 𝐿−limited subsets (or 𝐿−limited subsets of order 𝑝) in their dual are relatively weakly compact, are precisely the Grothendieck spaces. Moreover, it is established that a Banach lattice.𝑀 of some operator spaces has the disjoint limited 𝑝−Schur property if and only if all evaluation operators on 𝑀 is disjoint limited p-convergent.

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