José E. Galé

ON AMENABILITY AND GEOMETRY OF SPACES OF BOUNDED REPRESENTATIONS

Several differential geometric aspects of the space of representations of amenable Banach algebras are studied: differential structure, natural connection, geodesics, reductive structure, and so on. As an application we get a characterisation of amenable groups in terms of the existence of a reductive structure in that space.

Bounded degree of weakly algebraic topological Lie algebras

We prove in this paper that a weakly algebraic Lie algebraA which is also a topological Baire algebra over a complete non-discrete valuated fieldK must be in fact algebraic of bounded degree. Similar results are also proven forp-algebraic restricted Liep-algebras, and for algebraic non-associative algebras.

Universal objects in categories of reproducing kernels.

We continue our earlier investigation on generalized reproducing kernels, in connection with the complex geometry of

Reproducing Kernels and Positivity of Vector Bundles in Infinite Dimensions

C^*

H ∞ -functional calculus and models of Nagy–Foiaş type for sectorial operators

- algebra representations, by looking at them as the objects of an appropriate category. Thus the correspondence between reproducing

An analytic semigroup version of the Beurling-Helson theorem

(-*)

Linearly compact algebraic Lie algebras and coalgebraic Lie coalgebras

-kernels and the associated Hilbert spaces of sections of vector bundles is made into a functor. We construct reproducing

Transference for Banach space representations of nilpotent Lie groups. Part 1. Irreducible representations

(-*)

Extension problem and fractional operators: semigroups and wave equations

-kernels with universality properties with respect to the operation of pull-back. We show how completely positive maps can be regarded as pull-backs of universal ones linked to the tautological bundle over the Grassmann manifold of the Hilbert space

Functional Calculus for Infinitesimal Generators of Holomorphic Semigroups

\ell^2({\mathbb N})