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Compact diagonal linear operators on Banach spaces with unconditional bases. (English) Zbl 0792.47022

Using the concept of weak uniform continuity, this paper shows that a diagonal linear operator \(T: E\to F\) is compact if and only if its entries tend to 0 (\(E\) and \(F\) are to be Banach spaces with equivalent normalized unconditional bases).

MSC:

47B07 Linear operators defined by compactness properties
47B37 Linear operators on special spaces (weighted shifts, operators on sequence spaces, etc.)
46B15 Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces
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