Weak compactness of certain sets of measures

Sequential Compactness for the Weak Topology of Vector Measures in Certain Nuclear Spaces

We give a sequential compactness criterion for the weak topology of vector measures with values in certain nuclear spaces, such as the space S of all rapidly decreasing, infinitely differentiable functions, the space D of all test functions, and the strong duals of those spaces. This result contains Prokhorov–LeCam’s criterion for real measures and applies to cases which are not covered by März...

Weak compactness in certain star-shift invariant subspaces

The context of much of the work in this paper is that of a backward-shift invariant subspace of the form KB :1⁄4 HðDÞ~BHðDÞ; where B is some infinite Blaschke product. We address (but do not fully answer) the question: For which B can one find a (convergent) sequence f fngn1⁄41 in KB such that the sequence of real measures flog j fnjdyg N n1⁄41 converges weak-star to some nontrivial singular me...

Weak Compactness of the Set of ε-Extensions

Homomorphism Weak amenability of certain Banach algebras

In this paper we introduce the notion of $varphi$-commutativity for a Banach algebra $A$, where $varphi$ is a continuous homomorphism on $A$ and study the concept of $varphi$-weak amenability for $varphi$-commutative Banach algebras. We give an example to show that the class of $varphi$-weakly amenable Banach algebras is larger than that of weakly amenable commutative Banach algebras. We charac...

Compactness of isospectral sets

© Séminaire de Théorie spectrale et géométrie (Grenoble), 1991, tous droits réservés. L’accès aux archives de la revue « Séminaire de Théorie spectrale et géométrie » implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/legal.php). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fi...