The ασ-Approximation Property and Its Related Operator Ideals

被引：0

作者：

Kim, Ju Myung ^{[1
]}

机构：

[1] Sejong Univ, Dept Math & Stat, Seoul 05006, South Korea

来源：

MATHEMATICS | 2024年 / 12卷 / 13期

关键词：

tensor norm; approximation property; operator ideal; APPROXIMATION;

D O I：

10.3390/math12132006

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we study the sigma-tensor norm (alpha(sigma)), the absolutely tau-summing operator and the sigma-nuclear operator. We characterize the alpha sigma-approximation property in terms of some density of the space of absolutely tau-summing operators. When X* or Y*** has the approximation property, we prove that an operator T from X to Y is sigma-nuclear if the adjoint of T is sigma-nuclear.

引用

页数：9

共 10 条

[1] ON THE APPROXIMATION PROPERTIES FOR THE SPACE H-INFINITY [J].

BOURGAIN, J ;

REINOV, O .

MATHEMATISCHE NACHRICHTEN, 1985, 122 :19-27

[2]

Defant A., 1993, Tensor Norms and Operator Ideals

[3]

Diaz J.C., 1990, Collect. Math, V41, P217

[4]

DIESTEL J., 1995, ABSOLUTELY SUMMING O

[5]

Grothendieck A., 1955, Produits tensoriels topologiques et espaces nucleaires

[6] The Ideal of σ-Nuclear Operators and Its Associated Tensor Norm [J].

Kim, Ju Myung ;

Lee, Keun Young .

MATHEMATICS, 2020, 8 (07)

[7] Grothendieck's nuclear operator theorem revisited with an application to p-null sequences [J].

Oja, Eve .

JOURNAL OF FUNCTIONAL ANALYSIS, 2012, 263 (09) :2876-2892

[8]

Pietsch A., 1980, OPERATOR IDEALS

[9]

Ryan R., 2002, SPRINGER MONOGRAPHS, DOI DOI 10.1007/978-1-4471-3903-4

[10] APPROXIMATION HYPOTHESIS OF ORDER P IN BANACH SPACES AND APPROXIMATION OF ABSOLUTELY SUMMING P APPLICATIONS [J].

SAPHAR, P .

ISRAEL JOURNAL OF MATHEMATICS, 1972, 13 (3-4) :379-399

← 1 →