Multiplication Operator on Köthe Spaces: Measure of Non-compactness and Closed Range

René Erlin Castillo; Humberto Rafeiro; Julio C. Ramos-Fernández; Margot Salas-Brown

doi:10.1007/s40840-017-0562-0

Multiplication Operator on Köthe Spaces: Measure of Non-compactness and Closed Range

René Erlin Castillo
, Humberto Rafeiro
, Julio C. Ramos-Fernández
, Margot Salas-Brown

Research output: Contribution to journal › Article › peer-review

11 Citations (Scopus)

Abstract

We calculate the measure of non-compactness of the multiplication operator M_u acting on non-atomic Köthe spaces. We show that all bounded below multiplication operators acting on Köthe spaces are surjective and therefore bijective and we give some new characterizations about closedness of the range of M_u acting on Köthe spaces.

Original language	English
Pages (from-to)	1523-1534
Number of pages	12
Journal	Bulletin of the Malaysian Mathematical Sciences Society
Volume	42
Issue number	4
DOIs	https://doi.org/10.1007/s40840-017-0562-0
Publication status	Published - Jul 15 2019
Externally published	Yes

Keywords

Banach lattice
Köthe spaces
Multiplication operator

ASJC Scopus subject areas

General Mathematics

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10.1007/s40840-017-0562-0

Cite this

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abstract = "We calculate the measure of non-compactness of the multiplication operator Mu acting on non-atomic K{\"o}the spaces. We show that all bounded below multiplication operators acting on K{\"o}the spaces are surjective and therefore bijective and we give some new characterizations about closedness of the range of Mu acting on K{\"o}the spaces.",

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T2 - Measure of Non-compactness and Closed Range

AU - Castillo, René Erlin

AU - Rafeiro, Humberto

AU - Ramos-Fernández, Julio C.

AU - Salas-Brown, Margot

PY - 2019/7/15

Y1 - 2019/7/15

N2 - We calculate the measure of non-compactness of the multiplication operator Mu acting on non-atomic Köthe spaces. We show that all bounded below multiplication operators acting on Köthe spaces are surjective and therefore bijective and we give some new characterizations about closedness of the range of Mu acting on Köthe spaces.

AB - We calculate the measure of non-compactness of the multiplication operator Mu acting on non-atomic Köthe spaces. We show that all bounded below multiplication operators acting on Köthe spaces are surjective and therefore bijective and we give some new characterizations about closedness of the range of Mu acting on Köthe spaces.

KW - Banach lattice

KW - Köthe spaces

KW - Multiplication operator

UR - https://www.scopus.com/pages/publications/85067416651

UR - https://www.scopus.com/pages/publications/85067416651#tab=citedBy

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AN - SCOPUS:85067416651

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JF - Bulletin of the Malaysian Mathematical Sciences Society

IS - 4

ER -

Multiplication Operator on Köthe Spaces: Measure of Non-compactness and Closed Range

Abstract

Keywords

ASJC Scopus subject areas

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