## A note on relative compactness in $$K(X,Y)$$.(English)Zbl 1359.46017

Let $$X$$ and $$Y$$ be Banach spaces. The space of all compact operators between $$X$$ and $$Y$$ is denoted by $$K(X, Y)$$. In this paper, the author reobtains a result of T. W. Palmer [Proc. Am. Math. Soc. 20, 101–106 (1969; Zbl 0165.47603)] for relatively compact subsets of $$K(X, Y)$$ by using a characterization of weakly precompact subsets of $$K(X,Y)$$ due to the author [Commentat. Math. Univ. Carol. 56, No. 3, 319–329 (2015; Zbl 1349.46019)]. Furthermore, some necessary and sufficient conditions for the Dunford-Pettis relatively compact property of the spaces $$K(X, Y)$$ and $$K(X, Y^*)$$ are given.

### MSC:

 46B28 Spaces of operators; tensor products; approximation properties 46B50 Compactness in Banach (or normed) spaces

### Citations:

Zbl 0165.47603; Zbl 1349.46019
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