On Odd Duals of a Banach Algebra as a Banach Algebra

Authors

  • Mina Ettefagh

Keywords:

Banach algebra, Arens product, spectrum, quasi-inverse

Abstract

It is known that even duals of a Banach algebra A with one of Arens products are Banach algebras, these products are natural multiplications extending the one on A. But the essence of A*is completely different. We investigate some algebraic and spectral properties of odd duals of A, by defning the products ⃝a, ⃝F as in [12]. We will show relations between these products and Arens products, weak or weak-starcontinuity, commutativity and unit elements of these algebras. Also we determine the spectrum and multiplier algebra for A*, and we calculate the quasi-inverses, spectrum and spectral radius for elements of these kinds of algebras.

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Published

2021-09-13

Issue

Vol. 16

Section

Vol. 16, No. 3, (2022)

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