Displaying similar documents to “Unconditional ideals of finite rank operators”

M ( r , s ) -ideals of compact operators

Rainis Haller, Marje Johanson, Eve Oja (2012)

Czechoslovak Mathematical Journal

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We study the position of compact operators in the space of all continuous linear operators and its subspaces in terms of ideals. One of our main results states that for Banach spaces X and Y the subspace of all compact operators 𝒦 ( X , Y ) is an M ( r 1 r 2 , s 1 s 2 ) -ideal in the space of all continuous linear operators ℒ ( X , Y ) whenever 𝒦 ( X , X ) and 𝒦 ( Y , Y ) are M ( r 1 , s 1 ) - and M ( r 2 , s 2 ) -ideals in ℒ ( X , X ) and ℒ ( Y , Y ) , respectively, with r 1 + s 1 / 2 > 1 and r 2 + s 2 / 2 > 1 . We also prove that the M ( r , s ) -ideal 𝒦 ( X , Y ) in ℒ ( X , Y ) is separably determined. Among others, our results complete and improve some well-known...

On subspaces of Banach spaces where every functional has a unique norm-preserving extension

Eve Oja, Märt Põldvere (1996)

Studia Mathematica

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Let X be a Banach space and Y a closed subspace. We obtain simple geometric characterizations of Phelps' property U for Y in X (that every continuous linear functional g ∈ Y* has a unique norm-preserving extension f ∈ X*), which do not use the dual space X*. This enables us to give an intrinsic geometric characterization of preduals of strictly convex spaces close to the Beauzamy-Maurey-Lima-Uttersrud criterion of smoothness. This also enables us to prove that the U-property of the subspace...