This paper is concerned with partially defined derivations on Banach algebras and particularly on C*-algebras and H*-algebras, a subject whose study was motivated by the question of time evolution and spatial translation in quantum physics (see [2, 7] for a full account of the theory). It is well known [4] that everywhere defined derivations on semisimple Banach algebras are automatically conti...

We answer, by counterexample, several open questions concerning algebras of operators on a Hilbert space. The answers add further weight to the thesis that, for many purposes, such algebras ought to be studied in the framework of operator spaces, as opposed to that of Banach spaces and Banach algebras. We also answer a natural question about automatic w*-continuity arising in the preceding pape...

Suppose that A and B are unital Banach algebras with units 1A and 1B , respectively, M is a unital Banach A−B-bimodule, T =   A M 0 B   is the triangular Banach algebra, X is a unital T -bimodule, XAA = 1AX1A, XBB = 1BX1B , XAB = 1AX1B and XBA = 1BX1A. Applying two nice long exact sequences related to A, B, T , X, XAA, XBB , XAB and XBA we establish some results on (co)homology of triangu...

Several results are proved concerning representations of multiplier algebras that arise as extensions of representations of underlying Banach algebras. These results are then used to rederive Kisyński’s generalisation of the Hille–Yosida theorem and to establish two generalisations of the Trotter–Kato theorem, one of which, involving Banach bundles, is abstract and the other is classical in cha...

Let A be a Banach algebra. We call a pair (G,A) a Gelfand theory for A if the following axioms are satisfied: (G 1) A is a C∗-algebra, and G : A → A is a homomorphism; (G 2) the assignment L 7→ G−1(L) is a bijection between the sets of maximal modular left ideals of A and A, respectively; (G 3) for each maximal modular left ideal L of A, the linear map GL : A/G−1(L) → A/L induced by G has dense...

In this paper, we define the first topological (σ, τ)-cohomology group and examine vanishing of the first (σ, τ)-cohomology groups of certain triangular Banach algebras. We apply our results to study the (σ, τ)-weak amenability and (σ, τ)-amenability of triangular Banach algebras.

In the present paper, the Hyers-Ulam stability and also the superstability of double centralizers and multipliers on Banach algebras are established by using a fixed point method. With this method, the condition of without order on Banach algebras is no longer necessary.

In a previous note the author gave an example of a strong Ditkin algebra which does not have bounded relative units in the sense of Dales. In this note we investigate a certain family of Banach function algebras on the one point compactification of N, and see that within this family are many easier examples of strong Ditkin algebras without bounded relative units in the sense of Dales.

We use the Poisson integral formula in order to establish harmonic functional calculus for quotient involutive Banach algebras. We give several properties of this functional calculus. L.Waelbroeck’s holomorphic functional calculus is a special case of ours. We use our harmonic functional calculus to extend result of J.W.M.Ford to quotient involutive Banach algebras. L.WAELBROECK a montré dans [...