Simple construction of spaces without the Hahn-Banach extension property

Jerzy Kąkol

Displaying similar documents to “Simple construction of spaces without the Hahn-Banach extension property”

When $(E, σ (E, E^{'}))$ is a $D F$ -space?

Dorota Krassowska, Wiesƚaw Śliwa (1992)

Commentationes Mathematicae Universitatis Carolinae

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Let $(E, t)$ be a Hausdorff locally convex space. Either $(E, σ (E, E^{'}))$ or $(E^{'}, σ (E^{'}, E))$ is a $D F$ -space iff $E$ is of finite dimension (THEOREM). This is the most general solution of the problem studied by Iyahen [2] and Radenovič [3].

Strong topologies on vector-valued function spaces

Marian Nowak (2000)

Czechoslovak Mathematical Journal

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Let $(X, ∥ \cdot ∥_{X})$ be a real Banach space and let $E$ be an ideal of $L^{0}$ over a $σ$ -finite measure space $(Ø, Σ, μ)$ . Let $(X)$ be the space of all strongly $Σ$ -measurable functions $f Ø \to X$ such that the scalar function $\tilde{f}$ , defined by $\tilde{f} (ø) = {∥ f (ø) ∥}_{X}$ for $ø \in Ø$ , belongs to $E$ . The paper deals with strong topologies on $E (X)$ . In particular, the strong topology $β (E (X), E {(X)}_{n}^{\sim})$ ( $E {(X)}_{n}^{\sim} =$ the order continuous dual of $E (X)$ ) is examined. We generalize earlier results of [PC] and [FPS] concerning the strong topologies.

Embeddings of C(K) spaces into C(S,X) spaces with distortion strictly less than 3

Leandro Candido, Elói Medina Galego (2013)

Fundamenta Mathematicae

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In the spirit of the classical Banach-Stone theorem, we prove that if K and S are intervals of ordinals and X is a Banach space having non-trivial cotype, then the existence of an isomorphism T from C(K, X) onto C(S,X) with distortion $| | T | | | | T^{- 1} | |$ strictly less than 3 implies that some finite topological sum of K is homeomorphic to some finite topological sum of S. Moreover, if Xⁿ contains no subspace isomorphic to $X^{n + 1}$ for every n ∈ ℕ, then K is homeomorphic to S. In other words, we obtain a vector-valued...

Applications of some results of infinite-dimensional topology to the topological classification of operator images

Taras Banakh, Tadeusz Dobrowolski, Anatoliĭ Plichko

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This volume consists of three relatively independent articles devoted to the topological study of the so-called operator images and weak unit balls of Banach spaces. These articles are: “The topological classification of weak unit balls of Banach spaces” by T. Banakh, “The topological and Borel classification of operator images” by T. Banakh, T. Dobrowolski and A. Plichko, and “Operator images homeomorphic to $Σ^{ω}$ ” by T. Banakh. The articles summarize investigations that has been done by...

Displaying similar documents to “Simple construction of spaces without the Hahn-Banach extension property”

When ( E , σ ( E , E ' ) ) is a D F -space?

Strong topologies on vector-valued function spaces

Embeddings of C(K) spaces into C(S,X) spaces with distortion strictly less than 3

Applications of some results of infinite-dimensional topology to the topological classification of operator images

When $(E, σ (E, E^{'}))$ is a $D F$ -space?