S. Sherman has shown [4] that if the self adjoint elements of a C* algebra form a lattice under their natural ordering the algebra is necessarily commutative. In this note we extend this result to real Banach algebras with an identity and arbitrary Banach * algebras with an identity. The central fact for a real Banach algebra A is that if the positive cone is defined to be the uniform closure o...

In 1972, the late B. E. Johnson introduced the notion of an amenable Banach algebra and asked whether the Banach algebra B(E) of all bounded linear operators on a Banach space E could ever be amenable if dimE = ∞. Somewhat surprisingly, this question was answered positively only very recently as a by-product of the Argyros– Haydon result that solves the “scalar plus compact problem”: there is a...

Let S be a semigroup, and let ` (S) be the Banach algebra which is the semigroup algebra of S. We shall study the structure of this Banach algebra and of its second dual. We shall determine exactly when ` (S) is amenable as a Banach algebra, and shall discuss its amenability constant, showing that there are ‘forbidden values’ for this constant. The second dual of ` (S) is the Banach algebraM(βS...

In the present paper we study the structure of a Banach algebra B(A,Tg) generated by a certain Banach algebra A of operators acting in a Banach space D and a group {Tg}g∈G of isometries of D such that TgAT −1 g = A. We investigate the interrelations between the existence of the expectation of B(A,Tg) onto A, topological freedom of the automorphisms of A induced by Tg and the dual action of the ...

Using the notion of a symmetric virtual diagonal for Banach algebra, we prove that algebra is symmetrically amenable if its second dual amenable. We introduce operator amenability in category completely contractive algebras as an analogue algebras. give some equivalent formulations and investigate hereditary properties show locally compact groups to Fourier algebra. Finally, discuss about Jorda...

In the present paper we continue the study of the structure of a Banach algebra B(A,Tg) generated by a certain Banach algebra A of operators acting in a Banach space D and a group {Tg}g∈G of isometries of D such that TgAT −1 g = A. We investigate the interrelations between the existence of the expectation of B(A,Tg) onto A, metrical freedom of the automorphisms of A induced by Tg and the dual a...

Introduction. The purpose of this paper is to study noncommutative C*algebras as Banach spaces. The Gelfand representation of an abelian C*-algebra as the algebra of all continuous complex-valued functions on its spectrum has made it possible to apply the techniques of measure theory and the topological properties of compact Hausdorff spaces to the study of such algebras. No such structure theo...

Several concepts for the localization of a frame are studied. The intrinsic localization of a frame is defined by the decay properties of its Gramian matrix. Our main result asserts that the canonical dual frame possesses the same intrinsic localization as the original frame. The proof relies heavily on Banach algebra techniques, in particular on recent spectral invariance properties for certai...

We use representations of a Banach algebra A to completely characterize all finite-dimensional left ideals in the dual of introverted subspaces of A∗ and in particular in the double dual A∗∗. We give sufficient conditions under which such ideals always exist and are direct sums of one-dimensional left ideals.

Let K be a (commutative) locally compact hypergroup with a left Haar measure. Let L1(K) be the hypergroup algebra of K and UCl(K) be the Banach space of bounded left uniformly continuous complex-valued functions on K. In this paper we show, among other things, that the topological (algebraic) center of the Banach algebra UCl(K)* is M(K), the measure algebra of K.