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 | |
| State | Published - 1993 |
Keywords
- Weakly uniformly continuous
- compact operators
- diagonal operators
- unconditional bases
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