Displaying similar documents to “Topologies of compact families on the ideal space of a Banach algebra”

Topologies on the space of ideals of a Banach algebra

Ferdinand Beckhoff (1995)

Studia Mathematica

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Some topologies on the space Id(A) of two-sided and closed ideals of a Banach algebra are introduced and investigated. One of the topologies, namely τ ∞ , coincides with the so-called strong topology if A is a C*-algebra. We prove that for a separable Banach algebra τ ∞ coincides with a weaker topology when restricted to the space Min-Primal(A) of minimal closed primal ideals and that Min-Primal(A) is a Polish space if τ ∞ is Hausdorff; this generalizes results from [1] and [5]. All subspaces...

Metrization of function spaces with the Fell topology

Hanbiao Yang (2012)

Commentationes Mathematicae Universitatis Carolinae

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For a Tychonoff space X , let ↓ C F ( X ) be the family of hypographs of all continuous maps from X to [ 0 , 1 ] endowed with the Fell topology. It is proved that X has a dense separable metrizable locally compact open subset if ↓ C F ( X ) is metrizable. Moreover, for a first-countable space X , ↓ C F ( X ) is metrizable if and only if X itself is a locally compact separable metrizable space. There exists a Tychonoff space X such that ↓ C F ( X ) is metrizable but X is not first-countable.

Operators determining the complete norm topology of C(K)

A. Villena (1997)

Studia Mathematica

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For any uniformly closed subalgebra A of C(K) for a compact Hausdorff space K without isolated points and x 0 ∈ A , we show that every complete norm on A which makes continuous the multiplication by x 0 is equivalent to ∥ · ∥ ∞ provided that x 0 - 1 ( λ ) has no interior points whenever λ lies in ℂ. Actually, these assertions are equivalent if A = C(K).

Fragmentability and compactness in C(K)-spaces

B. Cascales, G. Manjabacas, G. Vera (1998)

Studia Mathematica

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Let K be a compact Hausdorff space, C p ( K ) the space of continuous functions on K endowed with the pointwise convergence topology, D ⊂ K a dense subset and t p ( D ) the topology in C(K) of pointwise convergence on D. It is proved that when C p ( K ) is Lindelöf the t p ( D ) -compact subsets of C(K) are fragmented by the supremum norm of C(K). As a consequence we obtain some Namioka type results and apply them to prove that if K is separable and C p ( K ) is Lindelöf, then K is metrizable if, and only if, there is a countable...

Convex sets in Banach spaces and a problem of Rolewicz

A. Granero, M. Jiménez Sevilla, J. Moreno (1998)

Studia Mathematica

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Let B x be the set of all closed, convex and bounded subsets of a Banach space X equipped with the Hausdorff metric. In the first part of this work we study the density character of B x and investigate its connections with the geometry of the space, in particular with a property shared by the spaces of Shelah and Kunen. In the second part we are concerned with the problem of Rolewicz, namely the existence of support sets, for the case of spaces C(K).