Infinite matrices bounded on weighted ℓ1 spaces

Joseph J. Williams; Qiang Ye

doi:10.1016/j.laa.2013.02.023

Infinite matrices bounded on weighted ℓ¹ spaces

Joseph J. Williams
, Qiang Ye

Producción científica: Article › revisión exhaustiva

7 Citas (Scopus)

Resumen

This paper investigates conditions under which an infinite matrix will be bounded as a linear operator between two weighted ℓ¹ spaces, and examines the relationship between the matrix and the weight vectors. It is shown that every infinite matrix is bounded as an operator between two weighted ℓ¹ spaces, for suitable weights. Necessary conditions and separate sufficient conditions for an infinite matrix to be bounded on some weighted ℓ¹ space (with the same weight for its domain and range) are given. We then show a connection between these results and the classical Schur Test which gives a sufficient condition for an infinite matrix to be bounded on the standard ℓ² (Hilbert) space.

Idioma original	English
Páginas (desde-hasta)	4689-4700
Número de páginas	12
Publicación	Linear Algebra and Its Applications
Volumen	438
N.º	12
DOI	https://doi.org/10.1016/j.laa.2013.02.023
Estado	Published - jun 15 2013

Nota bibliográfica

Funding Information:
Corresponding author. E-mail addresses: [email protected] (J.J. Williams), [email protected] (Q. Ye). 1 Research of this author was supported in part by NSF under Grant DMS-0915062.

Financiación

Corresponding author. E-mail addresses: [email protected] (J.J. Williams), [email protected] (Q. Ye). 1 Research of this author was supported in part by NSF under Grant DMS-0915062.

Financiadores	Número del financiador
National Science Foundation Arctic Social Science Program	DMS-0915062

ASJC Scopus subject areas

Algebra and Number Theory
Numerical Analysis
Geometry and Topology
Discrete Mathematics and Combinatorics

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10.1016/j.laa.2013.02.023

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abstract = "This paper investigates conditions under which an infinite matrix will be bounded as a linear operator between two weighted ℓ1 spaces, and examines the relationship between the matrix and the weight vectors. It is shown that every infinite matrix is bounded as an operator between two weighted ℓ1 spaces, for suitable weights. Necessary conditions and separate sufficient conditions for an infinite matrix to be bounded on some weighted ℓ1 space (with the same weight for its domain and range) are given. We then show a connection between these results and the classical Schur Test which gives a sufficient condition for an infinite matrix to be bounded on the standard ℓ2 (Hilbert) space.",

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N2 - This paper investigates conditions under which an infinite matrix will be bounded as a linear operator between two weighted ℓ1 spaces, and examines the relationship between the matrix and the weight vectors. It is shown that every infinite matrix is bounded as an operator between two weighted ℓ1 spaces, for suitable weights. Necessary conditions and separate sufficient conditions for an infinite matrix to be bounded on some weighted ℓ1 space (with the same weight for its domain and range) are given. We then show a connection between these results and the classical Schur Test which gives a sufficient condition for an infinite matrix to be bounded on the standard ℓ2 (Hilbert) space.

AB - This paper investigates conditions under which an infinite matrix will be bounded as a linear operator between two weighted ℓ1 spaces, and examines the relationship between the matrix and the weight vectors. It is shown that every infinite matrix is bounded as an operator between two weighted ℓ1 spaces, for suitable weights. Necessary conditions and separate sufficient conditions for an infinite matrix to be bounded on some weighted ℓ1 space (with the same weight for its domain and range) are given. We then show a connection between these results and the classical Schur Test which gives a sufficient condition for an infinite matrix to be bounded on the standard ℓ2 (Hilbert) space.

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KW - Weighted sequence space

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