We prove that every surjective isometry from the unit sphere of space K(H), all compact operators on an arbitrary complex Hilbert H, onto real Banach Y can be extended to a linear K(H) Y. This is probably first example infinite dimensional non-commutative C*-algebra containing no unitaries and satisfying Mazur-Ulam property. also C*-algebras weakly JB*-triples satisfy

We study the interaction between various analytification functors, and a class of morphisms rings, called homotopy epimorphisms. An functor assigns to simplicial commutative algebra over ring $R$, along with choice Banach structure on monoid in monoidal model category ind-Banach $R$-modules. show that several analytifications relevant analytic geometry - such as Tate, overconvergent, Stein anal...

let a be a banach algebra and x be a banach a-bimodule. in this paper, we de ne a new product on a  x and generalize the module extension banach algebras. we obtain characterizations of arens regularity, commutativity, semisimplity, and study the ideal structure and derivations of this new banach algebra.

Let $ (A,| cdot |) $ be a real Banach algebra, a complex algebra $ A_mathbb{C} $ be a complexification of $ A $ and $ | | cdot | | $ be an algebra norm on  $ A_mathbb{C}  $  satisfying a simple condition together with the norm $ | cdot | $ on $ A$.  In this paper we first show that $ A^* $ is a real Banach $ A^{**}$-module if and only if $ (A_mathbb{C})^* $ is a complex Banach $ (A_mathbb{C})^{...

let a be a banach algebra. a is called ideally amenable if for every closed ideal i of a, the first cohomology group of a with coefficients in i* is trivial. we investigate the closed ideals i for which h1 (a,i* )={0}, whenever a is weakly amenable or a biflat banach algebra. also we give some hereditary properties of ideal amenability.

For a matrix over a complex commutative unital Banach algebra, necessary and suucient conditions are given for the existence of its group inverse, and more generally, its Drazin inverses. The conditions are easy to check and explicit formulas for the inverses are provided. Some properties of the inverses and an application to operator theory are discussed. This note is a continuation of an earl...

We investigate two systematic constructions of inverse-closed subalgebras of a given Banach algebra or operator algebra A, both of which are inspired by classical principles of approximation theory. The first construction requires a closed derivation or a commutative automorphism group on A and yields a family of smooth inverse-closed subalgebras of A that resemble the usual Hölder-Zygmund spac...

Let R be a prime ring of characteristic different from 2, C the extended centroid of R, and δ a generalized derivations of R. If [[δ(x), x], δ(x)] = 0 for all x ∈ R then either R is commutative or δ(x) = ax for all x ∈ R and some a ∈ C. We also obtain some related result in case R is a Banach algebra and δ is either continuous or spectrally

Let R be a unital semi-simple commutative complex Banach algebra, and let M(R) denote its maximal ideal space, equipped with the Gelfand topology. Sufficient topological conditions are given on M(R) for R to be a projective free ring, that is, a ring in which every finitely generated projective R-module is free. Several examples are included, notably the Hardy algebra H∞(X) of bounded holomorph...