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Abstract
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International Journal of Mathematics and Mathematical Sciences
Volume 16 (1993), Issue 4, Pages 823-824
doi:10.1155/S0161171293001048

Compact diagonal linear operators on Banach spaces with unconditional bases

Yun Sung Choi and Sung Guen Kim

Department of Mathematics, Pohang Institute of Science and Technology, Pohang, Korea

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.