Research Article

Generalized domination of ergodic elements in ordered Banach algebras

Published in: Quaestiones Mathematicae
Volume 47 , issue sup1 : To the memory of W.A.J. Luxemburg and his mathematical legacy , 2024 , pages: 305–317

DOI: 10.2989/16073606.2023.2287851

Author(s): S. Mouton Stellenbosch University, South Africa , A.D. Rabearivony Stellenbosch University, South Africa

Keywords: 46H05 , 46H10 , 47A10 , 47B65 , Ordered Banach algebra , ergodic element , spectrum , regular operator

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Abstract

Let A be an ordered Banach algebra and a, b ∈ A such that 0 ≤ a ≤ b. The domination problem involves finding natural conditions under which properties of b will be inherited by a. In [12] this problem was investigated for ergodic elements, where a ∈ A is ergodic if the sequence converges in A. In this paper we consider the more general problem where the assumption 0 ≤ a ≤ b is replaced by the weaker condition ±a ≤ b.

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