Wyniki wyszukiwania

Sortuj według:

Ogranicz wyniki do:

Johnson's projection, Kalton's property (M*), and M-ideals of compact operators

100%

Nygaard O., Põldvere M.

Studia Mathematica

2009

tom 195

nr 3

243-255

Let X and Y be Banach spaces. We give a "non-separable" proof of the Kalton-Werner-Lima-Oja theorem that the subspace 𝒦(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 how Johnson's projection P on 𝓛(X,Y)* applies to f ∈ 𝓛(X,Y)* when f is represented via a Borel (with respect to the relative weak* topology) measure on $\overline{B_{X**} ⊗ B_{Y*}}^{w*} ⊂ 𝓛(X,Y)*$: If Y* has the Radon-Nikodým property, then P "passes under the integral sign". Our basic theorem en route to this description-a structure theorem for Borel probability measures on $\overline{B_{X**} ⊗ B_{Y*}}^{w*}$-also yields a description of 𝒦(X,Y)* due to Feder and Saphar. Second, we show that property (M*) for X is equivalent to every functional in $\overline{B_{X**} ⊗ B_{X*}}^{w*}$ behaving as if 𝒦(X,X) were an M-ideal in 𝓛(X,X).

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

100%

Oja E., Põldvere M.

Studia Mathematica

1995-1996

tom 117

nr 3

289-306

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 K(E,F) of compact operators from a Banach space E to a Banach space F in the corresponding space L(E,F) of all operators implies the U-property for F in F** whenever F is isomorphic to a quotient space of E.

Ograniczanie wyników

2 Studia Mathematica

2 Põldvere M.

1 Nygaard O.

1 Oja E.

1 2009

1 1996

Wyniki wyszukiwania

Johnson's projection, Kalton's property (M*), and M-ideals of compact operators

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