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

Colloquium Mathematicae (2015)

- Volume: 138, Issue: 2, page 255-269
- ISSN: 0010-1354

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topIoana Ghenciu. "Weak precompactness and property (V*) in spaces of compact operators." Colloquium Mathematicae 138.2 (2015): 255-269. <http://eudml.org/doc/283616>.

@article{IoanaGhenciu2015,

abstract = {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*).},

author = {Ioana Ghenciu},

journal = {Colloquium Mathematicae},

keywords = {weakly precompact sets; spaces of operators; compact operators; property },

language = {eng},

number = {2},

pages = {255-269},

title = {Weak precompactness and property (V*) in spaces of compact operators},

url = {http://eudml.org/doc/283616},

volume = {138},

year = {2015},

}

TY - JOUR

AU - Ioana Ghenciu

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

JO - Colloquium Mathematicae

PY - 2015

VL - 138

IS - 2

SP - 255

EP - 269

AB - 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*).

LA - eng

KW - weakly precompact sets; spaces of operators; compact operators; property

UR - http://eudml.org/doc/283616

ER -

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