The Schur property on projective and injective tensor products

被引：0

作者：

Botelho, Geraldo ^{[1
]}

Rueda, Pilar ^{[2
]}

机构：

[1] Univ Fed Uberlandia, Fac Matemat, BR-38400902 Uberlandia, MG, Brazil

[2] Univ Valencia, Dept Anal Matemat, E-46100 Valencia, Spain

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2009年 / 137卷 / 01期

关键词：

MULTILINEAR MAPPINGS; SPACES; POLYNOMIALS;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The problem of whether the Schur property is passed from a Banach space to its (symmetric) projective n-fold tensor product is reformulated in the language of polynomial ideals. As a result, a very closely related question is solved in the negative. It is also proved that the injective tensor product of infrabarrelled locally convex spaces with the Schur property has the Schur property as well.

引用

页码：219 / 225

页数：7

共 50 条

[1] Complexification of the projective and injective tensor products
van Zyl, Gusti
[J]. STUDIA MATHEMATICA, 2008, 189 (02) : 105 - 112
[2] ON THE EQUALITY OF INJECTIVE AND PROJECTIVE TENSOR-PRODUCTS
JARCHOW, H
JOHN, K
[J]. CZECHOSLOVAK MATHEMATICAL JOURNAL, 1988, 38 (03) : 464 - 472
[3] The positive Schur property on positive projective tensor products and spaces of regular multilinear operators
Geraldo Botelho
Qingying Bu
Donghai Ji
Khazhak Navoyan
[J]. Monatshefte für Mathematik, 2022, 197 : 565 - 578
[4] The positive Schur property on positive projective tensor products and spaces of regular multilinear operators
Botelho, Geraldo
Bu, Qingying
Ji, Donghai
Navoyan, Khazhak
[J]. MONATSHEFTE FUR MATHEMATIK, 2022, 197 (04): : 565 - 578
[5] The Grothendieck property for injective tensor products of Banach spaces
Ji, Donghai
Xue, Xiaoping
Bu, Qingying
[J]. CZECHOSLOVAK MATHEMATICAL JOURNAL, 2010, 60 (04) : 1153 - 1159
[6] The Grothendieck property for injective tensor products of Banach spaces
Donghai Ji
Xiaoping Xue
Qingying Bu
[J]. Czechoslovak Mathematical Journal, 2010, 60 : 1153 - 1159
[7] ON THE INTERPOLATION OF PROJECTIVE OR INJECTIVE TENSOR-PRODUCTS OF BANACH-SPACES
KOUBA, O
[J]. COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 1989, 309 (10): : 683 - 686
[8] ON THE INTERPOLATION OF INJECTIVE OR PROJECTIVE TENSOR-PRODUCTS OF BANACH-SPACES
KOUBA, O
[J]. JOURNAL OF FUNCTIONAL ANALYSIS, 1991, 96 (01) : 38 - 61
[9] Projective and injective tensor products of Banach L0-modules
Pasqualetto, Enrico
[J]. ANNALS OF FUNCTIONAL ANALYSIS, 2024, 15 (01)
[10] The alternative Dunford-Pettis property on projective tensor products
Peralta, AM
Villanueva, I
[J]. MATHEMATISCHE ZEITSCHRIFT, 2006, 252 (04) : 883 - 897

← 1 2 3 4 5 →