On rings and Banach algebras with skew derivations


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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