We construct a certain topological algebra Ext♯G∨X(χ) from a Deligne-Langlands parameter space X(χ) attached to the group of rational points of a connected split reductive algebraic group G over a non-Archimedean local field K. Then we prove the equivalence between the category of continuous modules of Ext♯G∨X(χ) and the category of unramified admissible modules of G(K) with a generalized infin...

Let A be an algebra, and let θ, φ be ring automorphisms of A. An additive mapping H : A → A is called a θ, φ -derivation if H xy H x θ y φ x H y for all x, y ∈ A. Moreover, an additive mapping F : A → A is said to be a generalized θ, φ -derivation if there exists a θ, φ derivation H : A → A such that F xy F x θ y φ x H y for all x, y ∈ A. In this paper, we investigate the superstability of gene...

Suppose that $A$ is a semi-simple and commutative Banach algebra. In this paper we try to characterize the character space of the Banach algebra $C_{rm{BSE}}(Delta(A))$ consisting of all  BSE-functions on $Delta(A)$ where $Delta(A)$ denotes the character space of $A$. Indeed, in the case that $A=C_0(X)$ where $X$ is a non-empty locally compact Hausdroff space, we give a complete characterizatio...

For locally compact groups all actions on a standard measure algebra have a spatial realization. For many Polish groups this is no longer the case. However, we show here that for non-archimedean Polish groups all measure algebra actions do have spatial realizations. In the other direction we show that an action of a Polish group is whirly (“ergodic at the identity”) if and only if it admits no ...

This study deals with an establishment of some common fixed point theorems for weak sub sequential continuous and compatibility of type (E) maps via C-class functions in a non Archimedean Menger Probabilistic Metric space.

We prove that all proper rigid-analytic spaces with “enough” algebraically independent meromorphic functions are algebraic (in the sense of proper algebraic spaces). This is a non-archimedean analogue of a result of Artin over C.

A C *-algebra A is called an ideal C * -algebra (or equally a dual algebra) if it is an ideal in its bidual A**. M.C.F. Berglund proved that subalgebras and quotients of ideal C*-algebras are also ideal C*-algebras, that a commutative C *-algebra A is an ideal C *-algebra if and only if it is isomorphicto C (Q) for some discrete space ?. We investigate ideal J*-algebras and show that the a...

A non-Archimedean antiderivational line analog of the Cauchy-type line integration is defined and investigated over local fields. Classes of non-Archimedean holomorphic functions are defined and studied. Residues of functions are studied; Laurent series representations are described. Moreover, non-Archimedean antiderivational analogs of integral representations of functions and differential for...

Let D be a division algebra for a non-Archimedean local field. Given an irreducible representation π of GL2(D), we describe its restriction to the diagonal subgroup D∗ × D∗. The description is in terms of the structure of the twisted Jacquet module of the representation π. The proof involves Kirillov theory that we have developed earlier in joint work with Dipendra Prasad. The main result on re...