Displaying similar documents to “Topologies on the space of ideals of a Banach algebra”

Topologies of compact families on the ideal space of a Banach algebra

Ferdinand Beckhoff (1996)

Studia Mathematica

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Let be a family of compact sets in a Banach algebra A such that is stable with respect to finite unions and contains all finite sets. Then the sets U ( K ) : = I ∈ I d ( A ) : I ∩ K = ∅ , K ∈ define a topology τ() on the space Id(A) of closed two-sided ideals of A. is called normal if I i → I in (Id(A),τ()) and x ∈ A╲I imply l i m i n f i ∥ x + I i ∥ > 0 . (1) If the family of finite subsets of A is normal then Id(A) is locally compact in the hull kernel topology and if moreover A is separable then Id(A) is second countable. (2) If the family of 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).

Banach spaces, à la recherche du temps perdu.

Jesús M. Fernández Castillo (2000)

Extracta Mathematicae

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What follows is the opening conference of the late night seminar at the III Conference on Banach Spaces held at Jarandilla de la Vera, Cáceres. Maybe the reader should not take everything what follows too seriously: after all, it was designed for a friendly seminar, late in the night, talking about things around a table shared by whisky, preprints and almonds. Maybe the reader should not completely discard it. Be as it may, it seems to me by now that everything arrives in the nick of...