In this paper we describe the commutant of an arbitrary subalgebra A of the algebra of functions on a set X in a crossed product of A with the integers, where the latter act on A by a composition automorphism defined via a bijection of X . The resulting conditions which are necessary and sufficient for A to be maximal abelian in the crossed product are subsequently applied to situations where t...

We define new symbol classes for pseudodifferential operators and investigate their pseudodifferential calculus. The symbol classes are parametrized by commutative convolution algebras. To every solid convolution algebraA over a lattice Λ we associate a symbol class M. Then every operator with a symbol in M is almost diagonal with respect to special wave packets (coherent states or Gabor frames...

For each triple of positive numbers p,q,r ≥ 1 and each commutative C-algebra with identity 1 and the set s( ) of states on , the set r ( ) of all matrices A = [ajk] over such that φ[A [r] ] := [φ(|ajk|r )] defines a bounded operator from p to q for all φ ∈ s( ) is shown to be a Banach algebra under the Schur product operation, and the norm ||A|| = |||A|||p,q,r = sup{||φ[A[r] ]||1/r : φ ∈ s( )}....

Motivated by the Poisson Dixmier-Moeglin equivalence problem, a systematic study of commutative unitary rings equipped with biderivation, namely binary operation that is derivation in each argument, here begun, an eye toward geometry corresponding B-varieties. Foundational results about extending biderivations to localisations, algebraic extensions and transcendental are established. Resolving ...

In this paper,  pseudo-amenability and pseudo-Connes amenability of weighted semigroup algebra $ell^1(S,omega)$ are studied. It is proved that pseudo-Connes amenability and pseudo-amenability of weighted group algebra $ell^1(G,omega)$ are the same. Examples are given to show that the class of $sigma$-Connes amenable dual Banach algebras is larger than that of Connes amenable dual Banach algebras.

in this paper we study the concept of ph-biatness ofa banach algebra a, where ph is a continuous homomorphism on a.we prove that if ph is a continuous epimorphism on a and a hasa bounded approximate identity and a is ph- biat, then a is ph-amenable. in the case where ph is an isomorphism on a we showthat the ph- amenability of a implies its ph-biatness.

The infinite-dimensional analogues of the classical general linear group appear as groups of invertible elements of Banach algebras. Mappings of these groups onto themselves that extend to affine mappings of the ambient Banach algebra are shown to be linear exactly when the Banach algebra is semi-simple. The form of such linear mappings is studied when the Banach algebra is a C*-algebra.

The separating space of a derivation onA is a separating ideal [2, Chapter 5]; it also satisfies the same property for the left products. The following assertions are of the most famous conjectures about derivations on Banach algebras: (C1) every derivation on a Banach algebra has a nilpotent separating ideal; (C2) every derivation on a semiprime Banach algebra is continuous; (C3) every derivat...

first we show that the cosets of a fuzzy ideal μ in a bck-algebrax form another bck-algebra  x/μ (called the fuzzy quotient bck-algebra of x by μ). also we show thatx/μ is a fuzzy partition of x and we prove several some isomorphism theorems. moreover we prove that if the associated fuzzy similarity relation of a fuzzy partition p of a commutative bck-algebra iscompatible, then p is a fuzzy quo...