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- W2085385631 abstract "Let ( X , τ 1 ) and ( Y , τ 2 ) be two Hausdorff locally convex spaces with continuous duals X ′ and Y ′, respectively, L ( X , Y ) be the space of all continuous linear operators from X into Y , K ( X , Y ) be the space of all compact operators of L ( X , Y ). Let WOT and UOT be the weak operator topology and uniform operator topology on K ( X , Y ), respectively. In this paper, we characterize a full-invariant property of K ( X , Y ); that is, if the sequence space λ has the signed-weak gliding hump property, then each λ -multiplier WOT -convergent series ∑ i T i in K ( X , Y ) must be λ -multiplier convergent with respect to all topologies between WOT and UOT if and only if each continuous linear operator T :(X,τ 1 )→(λ β ,σ(λ β ,λ)) is compact. It follows from this result that the converse of Kalton's Orlicz–Pettis theorem is also true." @default.
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- W2085385631 date "2002-06-01" @default.
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- W2085385631 title "A full-invariant theorem and some applications" @default.
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- W2085385631 doi "https://doi.org/10.1016/s0022-247x(02)00077-x" @default.
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