Let G be a reductive group over a non-Archimedean local field. Then the canonical functor from the derived category of smooth tempered representations of G to the derived category of all smooth representations of G is fully faithful. Here we consider representations on bornological vector spaces. As a consequence, if G is semi-simple, V and W are tempered irreducible representations of G, and V...

In this work we provide a characterization of distinct types (linear and non-linear) maps between Banach spaces in terms the differentiability certain class Lipschitz functions. Our results are stated an abstract bornological non-linear framework. Restricted to linear case, can apply our compact, weakly-compact, limited completely continuous operators. Moreover, yield Gelfand-Phillips recover s...

We provide two new characterizations of bounded orthogonally additive polynomials from a uniformly complete vector lattice into convex bornological space using separately polynomial identities Kusraeva involving the root mean power and geometric mean. Furthermore, it is shown that on whenever positive cone. These results improve recent by G. Buskes author.

We review topologically Nistor’s computation of the homogeneous part of the periodic cyclic cohomology of crossed products Γ⋉A of torsion-free discrete groups Γ with a complex Γ-algebra A. We use periodic cyclic cohomology associated to bornological algebras. Let G be a complex connected semisimple Lie group and B be a minimal parabolic subgroup of G. Applied to torsion-free discrete subgroups ...

It is shown that every locally idempotent (locallym-pseudoconvex) Hausdorff algebra A with pseudoconvex vonNeumannbornology is a regular (respectively, bornological) inductive limit of metrizable locallym-(kB-convex) subalgebras AB of A. In the case where A, in addition, is sequentially BA-complete (sequentially advertibly complete), then every subalgebraAB is a locally m-(kB-convex) Fréchet al...