We prove a Corona type theorem with bounds for the Sarason algebra H∞ + C and determine its spectral characteristics, thus continuing a line of research initiated by N. Nikolski. We also determine the Bass, the dense, and the topological stable ranks of H∞ + C. To fix our setting, let A be a commutative unital Banach algebra with unit e and M(A) its maximal ideal space. The following concept of...

We describe new Banach (not C∗ !) algebras generated by Toeplitz operators which are commutative on each weighted Bergman space over the unit ball B, where n > 2. For n = 2 all these algebras collapse to the single C∗-algebra generated by Toeplitz operators with quasi-parabolic symbols. As a by-product, we describe the situations when the product of mutually commuting Toeplitz operators is a To...

We provide a negative solution to a question of M. Rieffel who asked if the right and left topological stable ranks of a Banach algebra must always agree. Our example is found amongst a class of nest algebras. We show that for many other nest algebras, both the left and right topological stable ranks are infinite. We extend this latter result to Popescu’s non-commutative disc algebras and to fr...

Let a compact group U act by automorphisms of a commutative regular and Wiener Banach algebra A. We study representations Ru of U on quotient spaces A/I(üj), where u> is an orbit of U in the Gelfand space X of A and L(uj) is the minimal closed ideal with hull w C X. The main result of the paper is: if A = AP(X) is a weighted Fourier algebra on a LCA group X = A with a subpolynomial weight p on ...

Abstract We study homotopy epimorphisms and covers formulated in terms of derived Tate’s acyclicity for commutative $C^*$-algebras algebras continuous functions valued non-Archimedean fields. prove that a epimorphism between precisely corresponds to closed immersion the compact Hausdorff topological spaces associated with them cover $C^*$-algebra space it by immersions admitting finite subcover...

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 ...

We study the stability of certain spectra under some algebraic conditions weaker than commutativity and we generalize many known commutative perturbation results. In particular, in a complex unital Banach algebra $$\mathcal {A},$$ prove that if $$x \in \hbox {comm}_{w}(a)$$ is nilpotent, then $$\sigma (x)=\sigma (x+a).$$ Among other things, {comm}(xy)\cup {comm}(yx)$$ or $$y\in for all $$x,y \m...