Gholamreza Abbaspour Tabadkan

The notation of generalized Bessel multipliers is obtained by a bounded operator on ℓ2 which is inserted between the analysis and synthesis operators. We show that various properties of generalized multipliers are closely related to their parameters, in particular, it will be shown that the membership of generalized Bessel multiplier in the certain operator classes requires that its symbol belongs in the same classes, in a special sense. Also, we give some examples to illustrate our results. As we shall see, generalized multipliers associated with Riesz bases are well-behaved, more precisely in this case multipliers can be easily composed and inverted. Special attention is devoted to the study of invertible generalized multipliers. Sufficient and/or necessary conditions for invertibility are determined. Finally, the behavior of these operators under perturbations is discussed. © 2018, Springer International Publishing AG, part of Springer Nature.

A Banach algebra A is called ideally amenable if H1(A, I*) = 0 for each closed ideal I of A. Let X be an A-B-module, we show that the triangular Banach algebra asociated to X is ideally amenable if and only if A and B are ideally amenable.

Let E, F be two Hilbert C*-modules over C*-algebras A and B respectively. In this paper, by the alternative fixed point theorem, we give the Hyers–Ulam–Rassias stability of the equation 〈U(x), U(y)〉 = φ(〈x, y〉) (x, y ∈ E), where U: E → F is a mapping and φ: A → B is an additive map. © 2010, Duke University Press. All rights reserved.