Unconditionally convergent series of compact operators. (English) Zbl 0686.46010

The author presents an essentially self-contained proof of a result of N. J. Kalton that a series of compact operators between Banach spaces is subseries convergent with respect to the weak operator topology if and only if it is subseries convergent with respect to the norm topology provided that the domain space does not contain a copy of \(\ell^{\infty}\).
Reviewer: T.Ando


46B15 Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces
47B06 Riesz operators; eigenvalue distributions; approximation numbers, \(s\)-numbers, Kolmogorov numbers, entropy numbers, etc. of operators
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