منابع مشابه
M-ideals of Compact Operators Intò P
We show for 2 p < 1 and subspaces X of quotients of L p with a 1-unconditional nite-dimensional Schauder decomposition that K (X; ` p) is an M-ideal in L(X; ` p).
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We investigate a variant of the compact metric approximation property which, for subspaces X of c0 , is known to be equivalent to K(X), the space of compact operators on X , being an A/-ideal in the space of bounded operators on X , L{X). Among other things, it is shown that an arbitrary Banach space X has this property iff K(Y, X) is an Af-ideal in L(Y, X) for all Banach spaces Y and, furtherm...
متن کاملJohnson’s Projection, Kalton’s Property (m∗), and M-ideals of Compact Operators
Let X and Y be Banach spaces. We give a “non-separable” proof of the Kalton-Werner-Lima-Oja theorem that the subspaceK(X, X) of compact operators forms an M -ideal in the space L(X, X) of all continuous linear operators from X to X if and only if X has Kalton’s property (M∗) and the metric compact approximation property. Our proof is a quick consequence of two main results. First, we describe h...
متن کاملFunctions of self-adjoint operators in ideals of compact operators
For self-adjoint operators A,B, a bounded operator J , and a function f : R → C, we obtain bounds in quasi-normed ideals of compact operators for the difference f(A)J − Jf(B) in terms of the operator AJ − JB. The focus is on functions f that are smooth everywhere except for finitely many points. A typical example is the function f(t) = |t|γ with γ ∈ (0, 1). The obtained results are applied to d...
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We investigate the structure of Gδ ideals of compact sets. We define a class of Gδ ideals of compact sets that, on the one hand, avoids certain phenomena present among general Gδ ideals of compact sets and, on the other hand, includes all naturally occurring Gδ ideals of compact sets. We prove structural theorems for ideals in this class, and we describe how this class is placed among all Gδ id...
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ژورنال
عنوان ژورنال: Illinois Journal of Mathematics
سال: 1993
ISSN: 0019-2082
DOI: 10.1215/ijm/1255987254