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Displaying similar documents to “Operators determining the complete norm topology of C(K)”

Transitivity for linear operators on a Banach space

Bertram Yood (1999)

Studia Mathematica

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Let G be the multiplicative group of invertible elements of E(X), the algebra of all bounded linear operators on a Banach space X. In 1945 Mackey showed that if x 1 , … , x n and y 1 , … , y n are any two sets of linearly independent elements of X with the same number of items, then there exists T ∈ G so that T ( x k ) = y k , k = 1 , … , n . We prove that some proper multiplicative subgroups of G have this property.

Simple construction of spaces without the Hahn-Banach extension property

Jerzy Kąkol (1992)

Commentationes Mathematicae Universitatis Carolinae

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An elementary construction for an abundance of vector topologies ξ on a fixed infinite dimensional vector space E such that ( E , ξ ) has not the Hahn-Banach extension property but the topological dual ( E , ξ ) ' separates points of E from zero is given.

Projections from L ( X , Y ) onto K ( X , Y )

Kamil John (2000)

Commentationes Mathematicae Universitatis Carolinae

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Generalization of certain results in [Sap] and simplification of the proofs are given. We observe e.g.: Let X and Y be Banach spaces such that X is weakly compactly generated Asplund space and X * has the approximation property (respectively Y is weakly compactly generated Asplund space and Y * has the approximation property). Suppose that L ( X , Y ) ≠ K ( X , Y ) and let 1 < λ < 2 . Then X (respectively Y ) can be equivalently renormed so that any projection P of L ( X , Y ) onto K ( X , Y ) has the sup-norm greater or equal to λ . ...

Uniqueness of the topology on L¹(G)

J. Extremera, J. F. Mena, A. R. Villena (2002)

Studia Mathematica

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Let G be a locally compact abelian group and let X be a translation invariant linear subspace of L¹(G). If G is noncompact, then there is at most one Banach space topology on X that makes translations on X continuous. In fact, the Banach space topology on X is determined just by a single nontrivial translation in the case where the dual group Ĝ is connected. For G compact we show that the problem of determining a Banach space topology on X by considering translation operators on X is...

The structure of Lindenstrauss-Pełczyński spaces

Jesús M. F. Castillo, Yolanda Moreno, Jesús Suárez (2009)

Studia Mathematica

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Lindenstrauss-Pełczyński (for short ℒ) spaces were introduced by these authors [Studia Math. 174 (2006)] as those Banach spaces X such that every operator from a subspace of c₀ into X can be extended to the whole c₀. Here we obtain the following structure theorem: a separable Banach space X is an ℒ-space if and only if every subspace of c₀ is placed in X in a unique position, up to automorphisms of X. This, in combination with a result of Kalton [New York J. Math. 13 (2007)], provides...

Theorems of Krein Milman type for certain convex sets of functions operators

Robert R. Phelps (1970)

Annales de l'institut Fourier

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Sufficient conditions are given in order that, for a bounded closed convex subset B of a locally convex space E , the set C ( X , B ) of continuous functions from the compact space X into B , is the uniformly closed convex hull in C ( X , E ) of its extreme points. Applications are made to the unit ball of bounded (or compact, or weakly compact) operators from certain Banach spaces into C ( X ) .

Holomorphic germs on Banach spaces

Chae Soo Bong (1971)

Annales de l'institut Fourier

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Let E and F be two complex Banach spaces, U a nonempty subset of E and K a compact subset of E . The concept of holomorphy type θ between E and F , and the natural locally convex topology 𝒯 ω , θ on the vector space ℋ θ ( U , F ) of all holomorphic mappings of a given holomorphy type θ from U to F were considered first by L. Nachbin. Motived by his work, we introduce the locally convex space ℋ θ ( K , F ) of all germs of holomorphic mappings into F around K of a given holomorphy type θ , and study its interplay with...