STRONG BANACH-SAKS OPERATORS

被引：0

作者：

Hajji, Mohamed ^{[1
]}

机构：

[1] Issat Kasserine, Dept Math & Comp Sci, BP 471, Kasserine 1200, Tunisia

来源：

METHODS OF FUNCTIONAL ANALYSIS AND TOPOLOGY | 2020年 / 26卷 / 04期

关键词：

Banach-Saks; Banach lattice; L-weakly compact; order continuous norm;

D O I：

10.31392/MFAT-npu26_4.2020.05

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we introduce a new class of operators, called strong Banach-Saks operators, related to the Banach-Saks and L-weakly compact operators. We first prove that every strong Banach-Saks operator from a Banach space Z into a Banach lattice F is Banach-Saks. Then we show that if F is order continuous, the notions of strong Banach-Saks and Banach-Saks operators coincide. Finally, we close this paper by a new characterization of order continuous Banach lattices.

引用

页码：341 / 347

页数：7

共 50 条

[41] REGULAR METHODS OF SUMMABILITY AND BANACH-SAKS PROPERTY
ERDOS, P
MAGIDOR, M
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1976, 59 (02) : 232 - 234
[42] BANACH-SAKS EXPONENT OF CERTAIN BANACH-SPACES OF SEQUENCES
RAKOV, SA
[J]. MATHEMATICAL NOTES, 1982, 32 (5-6) : 791 - 797
[43] The Banach-Saks property in rearrangement invariant spaces
Dodds, PG
Semenov, EM
Sukochev, FA
[J]. STUDIA MATHEMATICA, 2004, 162 (03) : 263 - 294
[44] The Banach-Saks index of some sequence spaces
A. I. Novikova
[J]. Siberian Mathematical Journal, 2010, 51 : 296 - 300
[45] The weak Banach-Saks property for function spaces
Curbera, Guillermo P.
Ricker, Werner J.
[J]. REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS, 2017, 111 (03) : 657 - 671
[46] Banach-Saks index in spaces with symmetric basis
Novikova, A. I.
Semenova, E. M.
Sukochev, F. A.
[J]. DOKLADY MATHEMATICS, 2008, 77 (03) : 396 - 397
[47] THE BANACH-SAKS PROPERTIES IN SPACES WITH SYMMETRICAL BASIS
OSTROVSKY, MI
[J]. DOPOVIDI AKADEMII NAUK UKRAINSKOI RSR SERIYA A-FIZIKO-MATEMATICHNI TA TECHNICHNI NAUKI, 1985, (08): : 12 - 14
[48] The Banach-Saks Properties in Orlicz-Lorentz Spaces
Kaminska, Anna
Lee, Han Ju
[J]. ABSTRACT AND APPLIED ANALYSIS, 2014,
[49] RANGE OF A VECTOR MEASURE HAS BANACH-SAKS PROPERTY
ANANTHARAMAN, R
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1977, 66 (01) : 183 - 184
[50] 3 SPACE PROBLEM FOR THE WEAK BANACH-SAKS PROPERTY
OSTROVSKII, MI
[J]. MATHEMATICAL NOTES, 1985, 38 (5-6) : 905 - 907

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