Let A be a Banach algebra, not necessarily unital, and let B be a closed subalgebra of A. We establish a connection between the Banach cyclic cohomology group HC(A) of A and the Banach B-relative cyclic cohomology group HCnB(A) of A. We prove that, for a Banach algebra A with a bounded approximate identity and an amenable closed subalgebra B of A, up to topological isomorphism, HC(A) = HCnB(A) ...

We show that if T is an isometry (as metric spaces) from an open subgroup of the invertible group A of a unital Banach algebra A onto an open subgroup of the invertible group B of a unital Banach algebra B, then T is extended to a real-linear isometry up to translation between these Banach algebras. We consider multiplicativity or unti-multiplicativity of the isometry. Note that a unital linear...

Let A be a C∗-algebra, and let X be a Banach A-bimodule. B. E. Johnson showed that local derivations from A into X are derivations. We extend this concept of locality to the higher cohomology of a C ∗-algebra and show that, for every n ∈ N, bounded local n-cocycles from A into X are n-cocycles. The study of the local properties of Hochschild cohomology of a Banach algebra was initiated by intro...

in this paper, the main results are:a study of the finitely generated mv-algebras of continuous functions from the n-th power of the unit real interval i to i;a study of hopfian mv-algebras; anda category-theoretic study of the map sending an mv-algebra as above to the range of its generators (up to a suitable form of homeomorphism).

It is a famous conjecture that every derivation on each Banach algebra leaves every primitive ideal of the algebra invariant. This conjecture is known to be true if, in addition, the derivation is assumed to be continuous. It is also known to be true if the algebra is commutative, in which case the derivation necessarily maps into the (Jacobson) radical. Because I. M. Singer and J. Wermer origi...

Abstract We present here a multiplicative version of the classical Kowalski–Słodkowski theorem, which identifies characters among collection all functionals on complex and unital Banach algebra A . In particular, we show that, if is $C^\star $ -algebra, $\phi :A\to \mathbb C continuous function satisfying \phi (x)\phi (y) \in \sigma (xy) for $x,y\in A$ (where $\sigma denotes spectrum), then eit...

In a recent paper, S.-E. Takahasi defined the notion of a BSE Banach module over a commutative Banach algebra A with bounded approximate identity. We show that the multiplier space &f(X) of X can be represented as a space of sections in a bundle of Banach spaces, and we use bundle techniques to obtain shorter proofs of various of Takahasi’s results on P-algebra modules and to answer several que...

Let  be a Banach algebra. Let  be linear mappings on . First we demonstrate a theorem concerning the continuity of double derivations; especially that all of -double derivations are continuous on semi-simple Banach algebras, in certain case. Afterwards we define a new vocabulary called “-higher double derivation” and present a relation between this subject and derivations and finally give some ...

In this paper, first, we introduce the new concept of 2-inner product on Banach modules over a $C^*$-algebra. Next,  we present the concept of 2-linear operators over a $C^*$-algebra. Our result improve  the main result of the paper  Z. Lewandowska.  In the final of this paper, we define the notions 2-adjointable mappings between 2-pre Hilbert C*-modules and prove supperstability of them ...