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The weak Phillips property

Ali Ülger (2001)

Colloquium Mathematicae

Let X be a Banach space. If the natural projection p:X*** → X* is sequentially weak*-weak continuous then the space X is said to have the weak Phillips property. We present several characterizations of the spaces having this property and study its relationships to other Banach space properties, especially the Grothendieck property.

Trivialization of 𝒞 ( X ) -algebras with strongly self-absorbing fibres

Marius Dadarlat, Wilhelm Winter (2008)

Bulletin de la Société Mathématique de France

Suppose A is a separable unital 𝒞 ( X ) -algebra each fibre of which is isomorphic to the same strongly self-absorbing and K 1 -injective C * -algebra 𝒟 . We show that A and 𝒞 ( X ) 𝒟 are isomorphic as 𝒞 ( X ) -algebras provided the compact Hausdorff space X is finite-dimensional. This statement is known not to extend to the infinite-dimensional case.

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