SOME RESULTS OF OPERATOR IDEALS ON s-TYPE |A, p| OPERATORS

被引：8

作者：

Maji, Amit ^{[1
]}

Srivastava, P. D. ^{[1
]}

机构：

[1] Indian Inst Technol Kharagpur, Dept Math, Kharagpur 721302, W Bengal, India

来源：

TAMKANG JOURNAL OF MATHEMATICS | 2014年 / 45卷 / 02期

关键词：

Approximation numbers; Kolmogorov numbers; operator ideals; s-numbers;

D O I：

10.5556/j.tkjm.45.2014.1297

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let s = (s(n)) be a sequence of s-numbers in the sense of Pietsch and A be an infinite matrix. This paper presents a generalized class A((s))-p of s-type |A, p| operators using s-number sequence which unifies many earlier well known classes. It is shown that the class A((s)) - p forms a quasi-Banach operator ideal under certain conditions on the matrix A. Moreover, the inclusion relations among the operator ideals as well as the inclusion relations among their duals are established. It is also proved that for the Ces` aro matrix of order 1, the operator ideal formed by approximation numbers is small for 1 < p < infinity.

引用

页码：119 / 136

页数：18

共 29 条

[21] Asymptotic formulae for s-numbers of a Sobolev embedding and a Volterra type operator
Edmunds, David E.
Lang, Jan
REVISTA MATEMATICA COMPLUTENSE, 2016, 29 (01): : 1 - 11
[22] Asymptotic formulae for s-numbers of a Sobolev embedding and a Volterra type operator
David E. Edmunds
Jan Lang
Revista Matemática Complutense, 2016, 29 : 1 - 11
[23] A Brief Survey on 1. Infinite-dimensional Schur-Horn Theorems and Infinite Majorization Theory with Applications to Operator Ideals 2. B(H)-subideals of Operators
Weiss, Gary
ALGEBRAIC METHODS IN FUNCTIONAL ANALYSIS: THE VICTOR SHULMAN ANNIVERSARY VOLUME, 2014, 233 : 281 - 294
[24] Grothendieck's nuclear operator theorem revisited with an application to p-null sequences
Oja, Eve
JOURNAL OF FUNCTIONAL ANALYSIS, 2012, 263 (09) : 2876 - 2892
[25] Estimates of the approximation numbers (s-numbers) for a class of differential operators of mixed type
Muratbekov, Mussakan
Igisinov, Sabit
ADVANCEMENTS IN MATHEMATICAL SCIENCES (AMS 2015), 2015, 1676
[26] Some properties of pre-quasi operator ideal of type generalized Cesaro sequence space defined by weighted means
Bakery, Awad A.
Mohammed, Mustafa M.
OPEN MATHEMATICS, 2019, 17 : 1703 - 1715
[27] On Narrow Operators from Lp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L_p$$\end{document} into Operator Ideals
Jinghao Huang
Marat Pliev
Fedor Sukochev
Mediterranean Journal of Mathematics, 2022, 19 (5)
[28] Ideals of mid p\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\varvec{p}}$$\end{document}-summing operators: a tensor product approach
Aleena Philip
Deepika Baweja
Advances in Operator Theory, 2023, 8 (2)
[29] The splitting property for (p,S)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(\,p,S)$$\end{document}-summing operators
Dumitru Popa
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 2017, 111 (1): : 167 - 175

← 1 2 3 →