Pseudospectra in Banach Jordan Algebras

Author : Abdelaziz Maouche

Abstract : The primary focus of this research is to broaden the concept of pseudo spectrum from operators or matrices to elements in a unital complex Banach Jordan algebra-transcending from the associative to the nonassociative setting. We introduce the notion of є-invertibility in a Banach Jordan algebra J, and establish the invariance of pseudospectra in a full subalgebra of J. Furthermore, we investigate the properties of the pseudo-spectrum of an element in a Banach Jordan algebra, we examine level sets of functions and pseudo-spectral bounds. In Section 5, the study extends to linear maps preserving pseudospctrum in Banach Jordan algebras. Section 6 is about the decomposition of some elements of a Banach Jordan algebra into simpler ones in localized subalgebras. Finally, Secion 7 is dedicated to the study of Roch-Silberman theorem in a JB-algebra.

Keywords : Banach Jordan algebra, є-invertibility, pseudospectrum, index of instability, level set function

Conference Name : International Conference on Functional Analysis and Operator Algebras (ICFAOA - 26)

Conference Place : Salzburg, Austria

Conference Date : 3rd Feb 2026