The positive Schur property on positive projective tensor products and spaces of regular multilinear operators

被引：3

作者：

Botelho, Geraldo ^{[1
]}

Bu, Qingying ^{[2
]}

Ji, Donghai ^{[3
]}

Navoyan, Khazhak ^{[1
]}

机构：

[1] Univ Fed Uberlandia, Fac Matemat, Uberlandia, MG, Brazil

[2] Univ Mississippi, Dept Math, Oxford, MS 38677 USA

[3] Harbin Univ Sci & Technol, Dept Math, Harbin 150080, Peoples R China

来源：

MONATSHEFTE FUR MATHEMATIK | 2022年 / 197卷 / 04期

关键词：

Banach lattices; Positive Schur property; Regular multilinear operators; Positive projective tensor product; DUNFORD-PETTIS OPERATORS; WEAK;

D O I：

10.1007/s00605-022-01677-2

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We characterize the positive Schur property in the positive projective tensor products of Banach lattices, we establish the connection with the weak operator topology and we give necessary and sufficient conditions for the space of regular multilinear operators/homogeneous polynomials taking values in a Dedekind complete Banach lattice to have the positive Schur property.

引用

页码：565 / 578

页数：14

共 50 条

[21] Linear operators and positive semidefiniteness of symmetric tensor spaces
ZiYan Luo
LiQun Qi
YinYu Ye
[J]. Science China Mathematics, 2015, 58 : 197 - 212
[22] Linear operators and positive semidefiniteness of symmetric tensor spaces
Luo ZiYan
Qi LiQun
Ye YinYu
[J]. SCIENCE CHINA-MATHEMATICS, 2015, 58 (01) : 197 - 212
[23] Separability for Positive Operators on Tensor Product of Hilbert Spaces
Hou, Jin Chuan
Chai, Jin Fei
[J]. ACTA MATHEMATICA SINICA-ENGLISH SERIES, 2021, 37 (06) : 893 - 910
[24] Regular multilinear operators on C(K) spaces
Bombal, F
Villanueva, I
[J]. BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 1999, 60 (01) : 11 - 20
[25] A NOTE ON THE POSITIVE SCHUR PROPERTY
WNUK, W
[J]. GLASGOW MATHEMATICAL JOURNAL, 1989, 31 : 169 - 172
[26] POSITIVE OPERATORS ON TENSOR-PRODUCTS WHICH ARE THE TENSOR PRODUCT OF THEIR RESTRICTIONS
PANNENBERG, M
[J]. ARCHIV DER MATHEMATIK, 1990, 55 (01) : 64 - 73
[27] On Positive Injective Tensor Products Being Grothendieck Spaces
Shaoyong Zhang
Zhaohui Gu
Yongjin Li
[J]. Indian Journal of Pure and Applied Mathematics, 2020, 51 : 1239 - 1246
[28] ON POSITIVE INJECTIVE TENSOR PRODUCTS BEING GROTHENDIECK SPACES
Zhang, Shaoyong
Gu, Zhaohui
Li, Yongjin
[J]. INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS, 2020, 51 (03): : 1239 - 1246
[29] A property of the output entropy of a positive map of spaces of nuclear operators
Shirokov, M. E.
[J]. MATHEMATICAL NOTES, 2010, 87 (3-4) : 449 - 451
[30] A property of the output entropy of a positive map of spaces of nuclear operators
M. E. Shirokov
[J]. Mathematical Notes, 2010, 87 : 449 - 451

← 1 2 3 4 5 →