Norm Estimates For Norm-Attainable Derivations in Banach Algebras

Abstract

The investigations of Norm-attainability in Hilbert spaces and derivations has been done for quite long. Norm-attainability conditions for elementary operators such as basic elementary operators and Jordan elementary operator has been done and results obtained. But norm-attainable conditions for derivations in Banach-algebras and norm-estimates that is upper and lower norm-estimates for derivations in Banach algebras has not been done. Objectively this study will: Establish norm-attainability conditions for derivations in Banach-algebras, determine upper and lower norm-estimates for norm-attainable derivations in Banach algebras. The research methods used involves use inequalities well known such as Cauchy Schwarz. Triangle,H''olders and Bessel's inequality. Technically, Direct sum decomposition, Polar decomposition and Tensor product methods were used. Results obtained from this study will be useful in quantum mechanics and in integration.