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On (Co)homology of triangular Banach algebras

Mohammad Sal Moslehian — 2005

Banach Center Publications

Suppose that A and B are unital Banach algebras with units $1_{A}$ and $1_{B}$ , respectively, M is a unital Banach A,B-module, $= [\begin{matrix} A & M \\ 0 & B \end{matrix}]$ is the triangular Banach algebra, X is a unital -bimodule, $X_{A A} = 1_{A} X 1_{A}$ , $X_{B B} = 1_{B} X 1_{B}$ , $X_{A B} = 1_{A} X 1_{B}$ and $X_{B A} = 1_{B} X 1_{A}$ . Applying two nice long exact sequences related to A, B, , X, $X_{A A}$ , $X_{B B}$ , $X_{A B}$ and $X_{B A}$ we establish some results on (co)homology of triangular Banach algebras.

On product of projections

Mohammad Sal Moslehian — 2004

Archivum Mathematicum

An operator with infinite dimensional kernel is positive iff it is a positive scalar times a certain product of three projections.

A Morita equivalence for Hilbert C*-modules

Maria Joiţa; Mohammad Sal Moslehian — 2012

Studia Mathematica

We introduce a notion of Morita equivalence for Hilbert C*-modules in terms of the Morita equivalence of the algebras of compact operators on Hilbert C*-modules. We investigate the properties of the new Morita equivalence. We apply our results to study continuous actions of locally compact groups on full Hilbert C*-modules. We also present an extension of Green's theorem in the context of Hilbert C*-modules.

Orthogonal constant mappings in isosceles orthogonal spaces

Madjid Mirzavaziri; Mohammad Sal Moslehian — 2006

Kragujevac Journal of Mathematics

Generalized induced norms

S. Hejazian; M. Mirzavaziri; Mohammad Sal Moslehian — 2007

Czechoslovak Mathematical Journal

Let $∥ \cdot ∥$ be a norm on the algebra $ℳ_{n}$ of all $n \times n$ matrices over $ℂ$ . An interesting problem in matrix theory is that “Are there two norms ${∥ \cdot ∥}_{1}$ and ${∥ \cdot ∥}_{2}$ on $ℂ^{n}$ such that $∥ A ∥ = max {∥ A x ∥_{2} ∥ x ∥_{1} = 1}$ for all $A \in ℳ_{n}$ ?” We will investigate this problem and its various aspects and will discuss some conditions under which ${∥ \cdot ∥}_{1} = {∥ \cdot ∥}_{2}$ .

Constructions preserving $n$ -weak amenability of Banach algebras

A. Jabbari; Mohammad Sal Moslehian; H. R. E. Vishki — 2009

Mathematica Bohemica

A surjective bounded homomorphism fails to preserve $n$ -weak amenability, in general. We however show that it preserves the property if the involved homomorphism enjoys a right inverse. We examine this fact for certain homomorphisms on several Banach algebras.

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Currently displaying 1 – 13 of 13

On (Co)homology of triangular Banach algebras

On product of projections

A Morita equivalence for Hilbert C*-modules

Orthogonal constant mappings in isosceles orthogonal spaces

Generalized induced norms

Constructions preserving $n$ -weak amenability of Banach algebras

On full Hilbert $C *$ -modules.

Hyers-Ulam-Rassias stability of generalized derivations.

An interview with Josip E. Pečarić.

Refinements of reverse triangle inequalities in inner product spaces.

On minimal norms on $M_{n}$ .

On automatic continuity of 3-holomorphisms on Banach algebras.

Reverse triangle inequality in Hilbert $C^{*}$ -modules.