Compact Diagonal Linear Operators on Banach Spaces with Unconditional Bases

Yun Sung Choi; Sung Guen Kim

doi:10.1155/S0161171293001048

Compact Diagonal Linear Operators on Banach Spaces with Unconditional Bases

Yun Sung Choi, Sung Guen Kim

Pohang University of Science and Technology

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

Abstract

Let E and F be Banach spaces with equivalent normalized unconditional bases. In this note we show that a bounded diagonal linear operator T : E → F is compact if and only if its entries tend to 0, using the concept of weak uniform continuity.

Original language	English
Pages (from-to)	823-824
Number of pages	2
Journal	International Journal of Mathematics and Mathematical Sciences
Volume	16
Issue number	4
DOIs	https://doi.org/10.1155/S0161171293001048
State	Published - 1993

Keywords

compact operators
diagonal operators
unconditional bases
Weakly uniformly continuous

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abstract = "Let E and F be Banach spaces with equivalent normalized unconditional bases. In this note we show that a bounded diagonal linear operator T : E → F is compact if and only if its entries tend to 0, using the concept of weak uniform continuity.",

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author = "Choi, {Yun Sung} and Kim, {Sung Guen}",

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AU - Choi, Yun Sung

AU - Kim, Sung Guen

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AB - Let E and F be Banach spaces with equivalent normalized unconditional bases. In this note we show that a bounded diagonal linear operator T : E → F is compact if and only if its entries tend to 0, using the concept of weak uniform continuity.

KW - compact operators

KW - diagonal operators

KW - unconditional bases

KW - Weakly uniformly continuous

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JO - International Journal of Mathematics and Mathematical Sciences

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Compact Diagonal Linear Operators on Banach Spaces with Unconditional Bases

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