A Remark on the Stability of Approximative Compactness
We study the stability of approximativeτ-compactness, whereτis the norm or the weak topology. LetΛbe an index set and for everyλ∈Λ,letYλbe a subspace of a Banach spaceXλ. For1≤p<∞, letX=⊕lpXλandY=⊕lpYλ. We prove thatY(resp.,BY) is approximativelyτ-compact inXif and only if, for everyλ∈Λ,Yλ(resp.,BYλ) is approximativelyτ-compact inXλ.
2020 ◽
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1971 ◽
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1973 ◽
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1993 ◽
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