Operators constructed by means of basic sequences and nuclear matrices-Reference-Cited by-同舟云学术

Operators constructed by means of basic sequences and nuclear matrices

Published:2019-12 Issue:1 Volume:2019 Page:
ISSN:1687-1847
Container-title:Advances in Difference Equations
language:en
Short-container-title:Adv Differ Equ

Author:

Morsy Ahmed,Faried Nashat,Harisa Samy A.,Nisar Kottakkaran Sooppy

Abstract

AbstractIn this work, we establish an approach to constructing compact operators between arbitrary infinite-dimensional Banach spaces without a Schauder basis. For this purpose, we use a countable number of basic sequences for the sake of verifying the result of Morrell and Retherford. We also use a nuclear operator, represented as an infinite-dimensional matrix defined over the space

$\ell _{1}$

ℓ1 of all absolutely summable sequences. Examples of nuclear operators over the space

$\ell _{1}$

ℓ1 are given and used to construct operators over general Banach spaces with specific approximation numbers.

Funder

Prince Sattam bin Abdulaziz University

Publisher

Springer Science and Business Media LLC

Subject

Applied Mathematics,Algebra and Number Theory,Analysis

Link

http://link.springer.com/content/pdf/10.1186/s13662-019-2445-1.pdf

Reference13 articles.

1. Graduate Texts in Mathematics;F. Albiac,2006

2. Bessaga, C., Pełczyński, A.: On basis and unconditional convergence of series in Banach spaces. Stud. Math. 17, 151–164 (1958) http://eudml.org/doc/216910

3. Faried, N., Abd El Kader, Z., Mehanna, A.A.: s-numbers of polynomials of shift operators on $\ell ^{p}$ spaces $1\leq p \leq \infty $. J. Egypt. Math. Soc. 1, 31–37 (1993)

4. Faried, N., Harisa, S.A.: Wide class of Banach spaces in which Grothendieck conjecture holds. Glob. J. Pure Appl. Math. 12(6), 5059–5077 (2016) http://www.ripublication.com/gjpam.htm

5. Knopp, K.: Theory and Application of Infinite Series. Blackie and Son Limited, London (1951)