Properties \((V)\) and \((wV)\) in projective tensor products (Q472532)

In the first part of this paper, the author studies the structure of weakly precompact sets \(H\) in the space of compact operators in \({\mathcal K}(X,Y^\ast)\). A sufficient condition is the point-wise weak relative compactness. Some papers of related interest include [\textit{A. Ülger}, Math. Proc. Camb. Philos. Soc. 111, No. 1, 143--150 (1992; Zbl 0776.47017)] and [\textit{A. Ülger}, J. Oper. Theory 37, No. 2, 371--378 (1997; Zbl 0894.47033)]. The author also gives necessary conditions under the stronger hypothesis that all operators are compact.