On the compactness and the essential norm of operators defined by infinite tridiagonal matrices-Reference-Cited by-同舟云学术

On the compactness and the essential norm of operators defined by infinite tridiagonal matrices

Published:2023-01-01 Issue:1 Volume:10 Page:
ISSN:2299-3282
Container-title:Concrete Operators
language:en
Short-container-title:

Author:

Caicedo Alexander¹,Ramos-Fernández Julio C.²,Salas-Brown Margot³

Affiliation:

1. Departamento de Ingeniería Electrónica, Pontificia Universidad Javeriana , 110231 Bogotá , Colombia

2. Facultad de Ciencias Matemáticas y Naturales, Universidad Distrital Francisco José de Caldas , 111611 Bogotá , Colombia

3. Programa de Matemáticas, Escuela de Ciencias Exactas e Ingeniería, Universidad Sergio Arboleda , 110231 Bogotá , Colombia

Abstract

Abstract In this article, all sequences

{\boldsymbol{u}}

{\boldsymbol{v}}

, and

{\boldsymbol{w}}

that define continuous and compact tridiagonal operators

T u , v , w

{T}_{u,v,w}

acting on the weighted sequence space

l β 2

{l}_{\beta }^{2}

were characterized. Additionally, the essential norm of this operator, and as an important consequence of our results, the essential norm of multiplication operator

M u

{M}_{u}

acting on

l β 2

{l}_{\beta }^{2}

spaces was calculated.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Analysis

Link

https://www.degruyter.com/document/doi/10.1515/conop-2022-0143/pdf

Reference11 articles.

1. R. L. Burden, Numerical analysis/Richard L. Burden, J. Douglas Faires, Annette M. Burden, Cengage Learning, Boston, MA, 10th ed., 2016.

2. M.-T. Chien and H. Nakazato, The numerical range of a tridiagonal operator, J. Math. Anal. Appl. 373 (2011), no. 1, 297–304.

3. G. Datt and N. Ohri, Toeplitz and weighted Toeplitz operators on weighted sequence spaces, Gulf J. Math. 5 (2017), 62–70.

4. M. L. Doan and L. H. Khoi, Hilbert spaces of entire functions and composition operators, Complex Anal. Oper. Theory 10 (2016), no. 1, 213–230.

5. M. González, A. Martinez-Abejón, and J. Pello, A survey on the perturbation classes problem for semi-Fredholm and Fredholm operators, Funct. Anal. Approx. Comput. 7 (2015), 75–87.