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On the convergence and unconditionally convergence of series of operators on Banach spaces. (English) Zbl 1071.47500

It has previously been shown that if \(T_i:X\to Y\) are bounded linear maps such that \(\Sigma_iT_i\) is subseries convergent in the Banach space of compact linear maps with respect to the weak operator topology and \(X^*\) contains no subspace isomorphic to \(\ell_\infty\), then \(\Sigma_i T_i\) is subseries convergent with respect to the norm topology. The authors of the present paper use matrix techniques to obtain weaker sufficient conditions on the convergence and unconditional convergence of series of compact operators.

MSC:

47A05 General (adjoints, conjugates, products, inverses, domains, ranges, etc.)
46B15 Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces
47B07 Linear operators defined by compactness properties
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