On rings and Banach algebras with skew derivations

doi:10.1285/i15900932v40n1p73

On rings and Banach algebras with skew derivations

N. Rehman

Abstract

In the present paper, we investigate the commutativity of a prime Banach algebra with skew derivations and prove that if $\Aa$ is prime Banach algebra and $\Aa$ has a nonzero continuous linear skew derivation $\f$ from $\Aa$ to $\Aa$ such that $[\f(\xa^{m}), \f(\ya^{n})] - [\xa^{m}, \ya^{n}] \in \z(\Aa)$ for an integers $m = m(\xa, \ya)>1$ and $n = n(\xa, \ya)>1$ and sufficiently many $\xa, \ya$ , then $\Aa$ is commutative.

DOI Code: 10.1285/i15900932v40n1p73

Keywords: Prime Banach algebra; skew derivation

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On rings and Banach algebras with skew derivations

Abstract