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