In this paper we use Nachbin’s holomorphy types to generalize some recent results concerning hypercyclic convolution operators on Fréchet spaces of entire functions of bounded type of infinitely many complex variables
Let be a Banach algebra. is called ideally amenable if for every closed ideal of , the first cohomology group of with coefficients in is zero, i.e. . Some examples show that ideal amenability is different from weak amenability and amenability. Also for , is called -ideally amenable if for every closed ideal of , . In this paper we find the necessary and sufficient conditions for a module extension Banach algebra to be 2-ideally amenable.
We characterize the UMD-property of a Banach space X by sequences of ideal norms associated with trigonometric orthonormal systems. The asymptotic behavior of those numerical parameters can be used to decide whether X is a UMD-space. Moreover, if this is not the case, we obtain a measure that shows how far X is from being a UMD-space. The main result is that all described sequences are not only simultaneously bounded but are also asymptotically equivalent.
This paper may be viewed as having two aims. First, we continue our study of algebras of operators on a Hilbert space which have a contractive approximate identity, this time from a more Banach-algebraic point of view. Namely, we mainly investigate topics concerned with the ideal structure, and hereditary subalgebras (or HSA's, which are in some sense a generalization of ideals). Second, we study properties of operator algebras which are hereditary subalgebras in their bidual, or equivalently which...