we study topological von neumann regularity and principal von neumann regularity of banach algebras. our main objective is comparing these two types of banach algebras and some other known banach algebras with one another. in particular, we show that the class of topologically von neumann regular banach algebras contains all $c^*$-algebras, group algebras of compact abelian groups and cer...

I show a basic Yoneda-like lemma relating strongly dinatural transformations and initial algebras. Further, I apply it to reprove known results about unique existence of uniform parameterized fixpoint operators.

Let g be a complex simple Lie algebra and b a fixed Borel subalgebra of g. We shall describe the abelian ideals of b in a uniform way, that is, independent of the classification of complex simple Lie algebras.

It is shown how to embed the polydisk algebras (finite and infinite ones) into the disk algebra A(D). As a consequence, one obtains uniform closed subalgebras of A(D) which have arbitrarily prescribed stable ranks.

since 2005 a new powerful invariant of an algebra has emerged using the earlier work of horvath, hethelyi, kulshammer and murray. the authors studied morita invariance of a sequence of ideals of the center of a nite dimensional algebra over a eld of nite characteristic. it was shown that the sequence of ideals is actually a derived invariant, and most recently a slightly modi ed version o...

We generalize all known results on rigidity of uniform Roe algebras to the setting arbitrary uniformly locally finite coarse spaces. For instance, we show that isomorphism between spaces whose contain only compact ghost projections implies base are coarsely equivalent. Moreover, if one has property A, then bijectively also provide a characterization for existence an embedding onto hereditary su...

The classical Wiener’s lemma and its various generalizations are important and have numerous applications in numerical analysis, wavelet theory, frame theory, and sampling theory. There are many different equivalent formulations for the classical Wiener’s lemma, with an equivalent formulation suitable for our generalization involving commutative algebra of infinite matrices W := {(a(j − j))j,j′...