We consider when certain Banach sequence algebras A on the set N are approximately amenable. Some general results are obtained, and we resolve the special cases where A = ` p for 1 ≤ p < ∞, showing that these algebras are not approximately amenable. The same result holds for the weighted algebras ` (ω).

We prove that a surjective isometry between the unit spheres of two uniform algebras is extended to real-linear algebras. It provides first positive solution Tingley's problem on Banach space, without being Hilbert consisting analytic functions.

In this paper, we establish the Hyers–Ulam–Rassias stability of ring homomorphisms and ring derivations on fuzzy Banach algebras.

We investigate generalized amenability and biflatness properties of various (operator) Segal algebras in both the group algebra, L (G), and the Fourier algebra, A(G), of a locally compact group, G. Barry Johnson introduced the important concept of amenability for Banach algebras in [20], where he proved, among many other things, that a group algebra L1(G) is amenable precisely when the locally ...

Let $S$ be an inverse semigroup and let $E$ be its subsemigroup of idempotents. In this paper we define the $n$-th module cohomology group of Banach algebras and show that the first module cohomology group $HH^1_{ell^1(E)}(ell^1(S),ell^1(S)^{(n)})$ is zero, for every odd $ninmathbb{N}$. Next, for a Clifford semigroup $S$ we show that $HH^2_{ell^1(E)}(ell^1(S),ell^1(S)^{(n)})$ is a Banach sp...

In this article we study two different generalizations of von Neumann regularity, namely strong topological regularity and weak regularity, in the Banach algebra context. We show that both are hereditary properties and under certain assumptions, weak regularity implies strong topological regularity. Then we consider strong topological regularity of certain concrete algebras. Moreover we obtain ...

in the present paper, the concepts of module (uniform) approximate amenability and contractibility of banach algebras that are modules over another banach algebra, are introduced. the general theory is developed and some hereditary properties are given. in analogy with the banach algebraic approximate amenability, it is shown that module approximate amenability and contractibility are the same ...

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...

The Haagerup norm ‖ · ‖h on the tensor product A ⊗ B of two C∗-algebras A and B is shown to be Banach space equivalent to either the Banach space projective norm ‖ · ‖γ or the operator space projective norm ‖ · ‖∧ if and only if either A or B is finite dimensional or A and B are infinite dimensional and subhomogeneous. The Banach space projective norm and the operator space projective norm are ...