We give explicit formulae for the continuous Hochschild and cyclic homology and cohomology of certain ⊗̂-algebras. We use well-developed homological techniques together with some niceties of the theory of locally convex spaces to generalize the results known in the case of Banach algebras and their inverse limits to wider classes of topological algebras. To this end we show that, for a continuou...

Over time the concept of hypercyclicity has been explored in different manners and contexts, gaining new forms applications. In particular when space an adjacent structure, we can always look for sets hypercyclic vectors compatible with that framework. this paper deal operators acting on Fréchet sequence algebras give criteria existence common disjoint algebras.

A Fréchet algebra endowed with a multiplicatively convex topology has two types of invariants: homotopy invariants (topological K-theory and periodic cyclic homology) and secondary invariants (multiplicative Ktheory and the non-periodic versions of cyclic homology). The first aim of this paper is to establish a Riemann-Roch-Grothendieck theorem which describes direct images for homotopy and sec...

The commutation principle of Ramirez, Seeger, and Sossa [13] proved in the setting of Euclidean Jordan algebras says that when the sum of a Fréchet differentiable function Θ(x) and a spectral function F (x) is minimized over a spectral set Ω, any local minimizer a operator commutes with the Fréchet derivative Θ′(a). In this paper, we extend this result to sets and functions which are (just) inv...

In this paper we present some factorization properties for unbounded local positive maps. We show that an map ? on the minimal tensor product of locally C?-algebras A and C?(DE), where DE is a Fréchet quantized domain, dominated by ??id forma ??id, ? ?. As application result, given ?: A? B, ??idMn? decomposable n?2 if only ? CP-map. Also, CCP-map unital C? -algebras ??? ???˜, ?˜ CCP- ?, wheneve...

In the paper, we study various countably generated algebras of entire analytic functions on complex Banach spaces and their homomorphisms. Countably often appear as symmetric with respect to a group symmetries, are interesting for possible applications. Some conditions existence topological isomorphisms between such obtained. We construct class algebras, where all normalized algebraic bases equ...