Weakly and weak* p-convergent operators

Saak Gabriyelyan

doi:10.2298/FIL2429239G

Weakly and weak* p-convergent operators

Saak Gabriyelyan

Department of Mathematics

Ben-Gurion University of the Negev

Research output: Contribution to journal › Article › peer-review

Abstract

Let p ∈ [1, ∞]. Being motivated by weakly p-convergent and weak* p-convergent operators between Banach spaces introduced by Fourie and Zeekoei, we introduce and study the classes of weakly p-convergent and weak* p-convergent operators between arbitrary locally convex spaces. Relationships between these classes of operators are given, and we show that they have ideal properties. Numerous characterizations of weakly p-convergent and weak* p-convergent operators are given.

Original language	American English
Pages (from-to)	10239-10252
Number of pages	14
Journal	Filomat
Volume	38
Issue number	29
DOIs	https://doi.org/10.2298/FIL2429239G
State	Published - 1 Jan 2024

Keywords

Locally convex space
limited set
p-(V*) set of Pełczyński
p-convergent operator
weak* p-convergent operator
weakly p-convergent operator

All Science Journal Classification (ASJC) codes

General Mathematics

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10.2298/FIL2429239G

Cite this

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year = "2024",

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doi = "10.2298/FIL2429239G",

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N2 - Let p ∈ [1, ∞]. Being motivated by weakly p-convergent and weak* p-convergent operators between Banach spaces introduced by Fourie and Zeekoei, we introduce and study the classes of weakly p-convergent and weak* p-convergent operators between arbitrary locally convex spaces. Relationships between these classes of operators are given, and we show that they have ideal properties. Numerous characterizations of weakly p-convergent and weak* p-convergent operators are given.

AB - Let p ∈ [1, ∞]. Being motivated by weakly p-convergent and weak* p-convergent operators between Banach spaces introduced by Fourie and Zeekoei, we introduce and study the classes of weakly p-convergent and weak* p-convergent operators between arbitrary locally convex spaces. Relationships between these classes of operators are given, and we show that they have ideal properties. Numerous characterizations of weakly p-convergent and weak* p-convergent operators are given.

KW - Locally convex space

KW - limited set

KW - p-(V) set of Pełczyński

KW - p-convergent operator

KW - weak p-convergent operator

KW - weakly p-convergent operator

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U2 - 10.2298/FIL2429239G

DO - 10.2298/FIL2429239G

M3 - Article

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VL - 38

SP - 10239

EP - 10252

JO - Filomat

JF - Filomat

IS - 29

ER -

Weakly and weak* p-convergent operators

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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