We give some properties of the Banach algebra of bounded operators (lp(α)) for 1≤ p≤∞, where lp(α)= (1/α)−1∗lp . Then we deal with the continued fractions and give some properties of the operator ∆h for h > 0 or integer greater than or equal to one mapping lp(α) into itself for p ≥ 1 real. These results extend, among other things, those concerning the Banach algebra Sα and some results on the c...

A crossed product is the functional analysts’ version of a skew group ring. Thus, if α : G→ Aut(A) is an action of a locally compact group G on a Banach algebra A, then a crossed product Banach algebra encodes the action of G on A, and its representation theory is related to pairs (u, π) consisting of a representation u of G and a representation π of A on the same Banach space such that ugπ(a)u...

These notes are for a series of lectures given in functional analysis during Winter term of 2015. The two influences of the presentation here are Banach Algebra Techniques in Operator Theory (2e) by Ronald G. Douglas and Lecture Notes on the Spectral Theorem by Dana P. Williams. The notes start with a presentation of the two facts about nets that are required for the subject matter at hand. We ...

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 consider the transitive linear maps on the operator algebra $b(x)$for a separable banach space $x$. we show if a bounded linear map is norm transitive on $b(x)$,then it must be hypercyclic with strong operator topology. also we provide a sot-transitivelinear map without being hypercyclic in the strong operator topology.

We consider an involutive automorphism of the conformal algebra and the resulting symmetric space. We display a new action of the conformal group which gives rise to this space. The space has an intrinsic symplectic structure, a group-invariant metric and connection, and serves as the model space for a new conformal gauge theory. ∗Electronic-mail: [email protected]

Symmetry breaking boundary conditions for WZW theories are discussed. We derive explicit formulae for the reflection coefficients in the presence of boundary conditions that preserve only an orbifold subalgebra with respect to an involutive automorphism of the chiral algebra. The characters and modular transformations of the corresponding orbifold theories are computed. Both inner and outer aut...

Let X,Y be locally compact Hausdorff spaces and M,N be Banach algebras. Let θ : C0(X,M) → C0(Y,N ) be a zero-product preserving bounded linear map with dense range. We show that θ is given by a continuous field of algebra homomorphisms from M into N if N is irreducible. As corollaries, such a surjective θ arises from an algebra homomorphism, provided thatM is a W*-algebra and N is a semi-simple...

For locally compact groups, Fourier algebras and Fourier-Stieltjes algebras have proved to be useful dual objects. They encode the representation theory of the group via the positive deenite functions on the group: positive deenite functions correspond to cyclic representations and span these algebras as linear spaces. They encode information about the algebra of the group in the geometry of th...

let $mathcal{a}$ be a banach algebra with bai and $e$ be an introverted subspace of $mathcal{a'}$.in this paper we study the quotient arens regularity of $mathcal{a}$ with respect to $e$ and prove that the group algebra $l^1(g)$ for a locally compact group $g$, is quotient arens regular with respect to certain introverted subspace $e$ of $l^infty(g)$.some related result are given as well.