Related papers: On some automatic continuity theorems

We obtain generalisations of some inequalities for positive unital linear maps on matrix algebra. This also provides several positive semidefinite matrices and we get some old and new inequalities involving the eigenvalues of a Hermitian…

We employ the theory of canonical extensions to study residuation algebras whose associated relational structures are functional, i.e., for which the ternary relations associated to the expanded operations admit an interpretation as…

A map is given showing that convolutions of independent random variables over a finite group and matrix multiplications of doubly stochastic matrices are homomorphic. As an application, a short proof is given to the theorem that the…

In this article we shall focus on the derivations on module extension of Banach algebras and determine the general structure of them. Then we obtain some results concerning the automatic continuity of these mappings.

We deal with the existing problem of filtered multiplicative bases of finite-dimensional associative algebras. For an associative algebra A over a field, we investigate when the property of having a filtered multiplicative basis is…

Algebraic operations are understood as topologiztion of algebra. They become an example of simplest convergence space. In our article the convergence is a arbitrary multivalued appointment. The continuity of some mapping between two…

In 2014, we determine the precise form of a continuous orthogonal form on a commutative real C$^*$-algebra. We also describe the general form of a (not-necessarily continuous) orthogonality preserving linear map between commutative unital…

We describe isomorphisms of groups of several periodic infinite matrices and isomorphisms of groups of invertible elements of unital locally matrix algebras.

Automatic presentations, also called FA-presentations, were introduced to extend finite model theory to infinite structures whilst retaining the solubility of fundamental decision problems. This paper studies FA-presentable algebras. First,…

In aperiodic order, non-periodic but "ordered" objects such as tilings, Delone sets, functions and measures are investigated. In this article we depict the common structure of these objects by using the general framework of abstract pattern…

Theory of representations of universal algebra is a natural development of the theory of universal algebra. In the book, I considered representation of universal algebra, diagram of representations and examples of representation. Morphism…

In this paper, we give a purely cohomological interpretation of the extension problem for associative algebras; that is the problem of extending an associative algebra by another associative algebra. We then give a similar interpretation of…

In this paper we study analogues of amenability for topological groups in the context of definable structures. We prove fixed point theorems for such groups. More importantly, we propose definitions for definable actions and continuous…

We completely classify the orientable infinite-type surfaces $S$ such that $\operatorname{PMap}(S)$, the pure mapping class group, has automatic continuity. This classification includes surfaces with noncompact boundary. In the case of…

Bilinear maps and their classifying tensor products are well-known in the theory of linear algebra, and their generalization to algebras of commutative monads is a classical result of monad theory. Motivated by constructions needed in…

We describe spectra of associative (not necessarily unital and not necessarily countable-dimensional) locally matrix algebras. We determine all possible spectra of locally matrix algebras and give a new proof of Dixmier-Baranov Theorem. As…

The theory of persistence modules is an emerging field of algebraic topology which originated in topological data analysis. In these notes we provide a concise introduction into this field and give an account on some of its interactions…

Let $X$ be an arbitrary set. Then a topology $t$ on $X$ is said to be completely useful if every upper semicontinuous linear (total) preorder $\precsim$ on $X$ can be represented by an upper semicontinuous real-valued order preserving…

Let A and B be normal matrices with coefficients that are continuous complex-valued functions on a topological space X that has the homotopy type of a CW complex, and suppose these matrices have the same distinct eigenvalues at each point…

We expand on some invariants used for classifying nonselfadjoint operator algebras. Specifically to nonselfadjoint operator algebras which have a conditional expectation onto a commutative diagonal we construct an edge-colored directed…