International Journal of Mathematics and Mathematical Sciences
Volume 16 (1993), Issue 4, Pages 823-824

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

Received 13 April 1992; Revised 3 July 1992

Copyright © 1993 Yun Sung Choi and Sung Guen Kim. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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