Approximation theoretical properties of M-ideals (Abstract)
-Structure (a survey)
Multipliers on complex Banach spaces
Kompakte Abbildungen in lokalkonvexen Vektorräumen und eine Anwendung auf das Fortsetzungsproblem stetiger affiner Funktionen.
On the Banach-Stone Theorem.
Reflexivität von Räumen stetiger affiner Funktionen.
Über die Lp-Struktur in A(K)-Räumen.
How to Obtain Vector-Valued Banach-Stone Theorems by Using M-Structure Methods.
On the principle of local reflexivity
We prove a version of the local reflexivity theorem which is, in a sense, the most general one: our main theorem characterizes the conditions which can be imposed additionally on the usual local reflexivity map provided that these conditions are of a certain general type. It is then shown how known and new local reflexivity theorems can be derived. In particular, the compatibility of the local reflexivity map with subspaces and operators is investigated.
-Struktur in Banachräumen
-Struktur in Banachräumen II
On Bárány's theorems of Carathéodory and Helly type
The paper begins with a self-contained and short development of Bárány’s theorems of Carathéodory and Helly type in finite-dimensional spaces together with some new variants. In the second half the possible generalizations of these results to arbitrary Banach spaces are investigated. The Carathéodory-Bárány theorem has a counterpart in arbitrary dimensions under suitable uniform compactness or uniform boundedness conditions. The proper generalization of the Helly-Bárány theorem reads as follows:...
On the geometry of spaces of K-valued operators
Operators which respect norm intervals
Products of n open subsets in the space of continuous functions on [0,1]
Let O₁,...,Oₙ be open sets in C[0,1], the space of real-valued continuous functions on [0,1]. The product O₁ ⋯ Oₙ will in general not be open, and in order to understand when this can happen we study the following problem: given f₁,..., fₙ ∈ C[0,1], when is it true that f₁ ⋯ fₙ lies in the interior of for all ε > 0 ? ( denotes the closed ball with radius ε and centre f.) The main result of this paper is a characterization in terms of the walk t ↦ γ(t): = (f₁(t),..., fₙ(t)) in ℝⁿ. It has to...
A selection theorem of Helly type and its applications
We prove an abstract selection theorem for set-valued mappings with compact convex values in a normed space. Some special cases of this result as well as its applications to separation theory and Hyers-Ulam stability of affine functions are also given.
An isomorphic Banach-Stone theorem
Banach spaces which are proper M-ideals
Strongly mixing sequences of measure preserving transformations
We call a sequence of measure preserving transformations strongly mixing if tends to for arbitrary measurable , . We investigate whether one can pass to a suitable subsequence such that almost surely for all (or “many”) integrable .
M-structure and the Banach-Stone theorem
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