Choi, Yun Sung; Kim, Sung Guen Compact diagonal linear operators on Banach spaces with unconditional bases. (English) Zbl 0792.47022 Int. J. Math. Math. Sci. 16, No. 4, 823-824 (1993). 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). Reviewer: J.Howard (Las Vegas) 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 Keywords:compact operators; weak uniform continuity; diagonal linear operator; normalized unconditional bases PDFBibTeX XMLCite \textit{Y. S. Choi} and \textit{S. G. Kim}, Int. J. Math. Math. Sci. 16, No. 4, 823--824 (1993; Zbl 0792.47022) Full Text: DOI EuDML