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

Swartz, Charles

Commentat. Math. Univ. Carol. 30, No. 2, 321-322 (1989).

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

MSC:

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

Keywords:

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