Weak precompactness and property (V*) in spaces of compact operators

• Autorzy: Ioana Ghenciu
• Języki publikacji: EN

Abstrakty

EN

We give sufficient conditions for subsets of compact operators to be weakly precompact. Let $L_{w*}(E*,F)$ (resp. $K_{w*}(E*,F)$) denote the set of all w* - w continuous (resp. w* - w continuous compact) operators from E* to F.
We prove that if H is a subset of $K_{w*}(E*,F)$ such that H(x*) is relatively weakly compact for each x* ∈ E* and H*(y*) is weakly precompact for each y* ∈ F*, then H is weakly precompact. We also prove the following results:
If E has property (wV*) and F has property (V*), then $K_{w*}(E*,F)$ has property (wV*).
Suppose that $L_{w*}(E*,F) = K_{w*}(E*,F)$. Then $K_{w*}(E*,F)$ has property (V*) if and only if E and F have property (V*).

Kategorie tematyczne

• 46B20: Geometry and structure of normed linear spaces
• 28B05: Vector-valued set functions, measures and integrals
• 46B28: Spaces of operators; tensor products; approximation properties

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2015
• Tom: 138
• Numer: 2
• Strony: 255-269

Daty

wydano

2015

Twórcy

autor

Ioana Ghenciu

• Department of Mathematics, University of Wisconsin-River Falls, River Falls, WI 54022, U.S.A.

Identyfikatory

DOI

10.4064/cm138-2-10