Related papers: On some automatic continuity theorems

We construct a class of positive linear maps on matrix algebras. We find conditions when these maps are atomic, decomposable and completely positive. We obtain a large class of atomic positive linear maps. As applications in quantum…

This paper is the first in a series of papers developing a functional-analytic theory of vertex (operator) algebras and their representations. For an arbitrary Z-graded finitely-generated vertex algebra (V, Y, 1) satisfying the standard…

We study the topological full group of ample groupoids over locally compact spaces. We extend Matui's definition of the topological full group from the compact, to the locally compact case. We provide two general classes of groupoids for…

We show that morphisms from n A_infinity-algebras to a single one are maps over an operad module with n+1 commuting actions of the operad A_infinity, whose algebras are conventional A_infinity-algebras. Similar statement holds for homotopy…

Starting from a description of various generalized function algebras based on sequence spaces, we develop the general framework for considering linear problems with singular coefficients or non linear problems. Therefore, we prove…

We employ the notions of `sequential function' and `interrogation' (dialogue) in order to define new partial combinatory algebra structures on sets of functions. These structures are analyzed using J. Longley's preorder-enriched category of…

Tate cohomology has been generalised by several authors using different constructions that have applications in group theory, ring theory and homotopical algebra. Therefore, there is a need for a uniform account that explains why their…

We investigate commutator operations on compatible uniformities of an algebra. We present a commutator operation for compatible uniformities of an algebra in a congruence-modular variety which extends the commutator on congruences, and…

We relate extensions of completely unitary VOAs and (commutative) Q-systems. As an application, we show that any unitary extension of a completely unitary VOA is completely unitary.

We give a sufficient condition on totally disconnected topological graphs such that their associated topological graph algebras are purely infinite.

Using representation theory techniques we prove that various spaces of derivations or one-sided multipliers over certain operator algebras are reflexive. A sample result: any bounded local derivation (local left multiplier) on an…

We describe automorphisms and derivations of several important associative and Lie algebras of infinite matrices over a field.

It is a well-known fact in K-theory that the rapidly decreasing matrices of countable size form an associative topological algebra whose set of quasi-invertible elements is open, and such that the quasi-inversion map is continuous. We…

Given a strictly positive measure, we characterize inner semicontinuous solid convex-valued mappings for which continuous functions which are selections almost everywhere are selections. This class contains continuous mappings as well as…

Associative algebras with involution over a field of zero characteristic are considered. It is proved that in this case for any finitely generated associative algebra with involution there exists a finite dimensional algebra with involution…

Topologies on algebraic and equational theories are used to define germ determined, near-point determined, and point determined rings of smooth functions, without requiring them to be finitely generated. It is proved, that any commutative…

The possibility of extending operations of topological and semitopological algebras to their Stone-\v{C}ech compactification and factorization of continuous functions through homomorphisms to metrizable algebras are investigated. Most…

Let E be a locally solid vector lattice. In this paper, we consider two particular vector subspaces of the space of all order bounded operators on E. With the aid of two appropriate topologies, we show that under some conditions, they…

In a recent work of Matteo Mio on compact quantitative equational theories (here compact means that all its consequences are derivable by means of finite proofs) convex algebras on the carrier set [0,1] whose operations are monotone and…

Using the notion of existentially closed structures, we obtain embedding theorems for groups and Lie algebras. We also prove the existence of some groups and Lie algebras with prescribed properties.