Cubic Derivations on Banach Algebras

2013/01/14 by Abasalt Bodaghi, Bodaghi, Abasalt
Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #math.FA

paper · pdf · doi:10.48550/arxiv.1301.2888

arxiv created 2013/01/14 · arxiv updated 2013/01/15

Abstract

Let A be a Banach algebra and X be a Banach A-bimodule. A mapping D :A\longrightarrow X is a cubic derivation if D is a cubic homogeneous mapping, that is D is cubic and D(λa)=λ³ D(a) for any complex number λ and all a∈ A, and D(ab)=D(a)⋅ b³ +a³⋅ D(b) for all a,b∈ A. In this paper, we prove the stability of a cubic derivation with direct method. We also employ a fixed point method to establish of the stability and the superstability for cubic derivations.

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