On generalized spectra in C*-algebras of operators over C*-algebras

TL;DR

This paper explores generalized spectra of various classes of operators on modules over unital C*-algebras, providing descriptions and properties of these spectra.

Contribution

It introduces and analyzes new types of generalized spectra for operators on modules over C*-algebras, expanding spectral theory in this context.

Findings

Descriptions of generalized spectra for shift, self-adjoint, unitary, and normal operators.

Properties and characterizations of these spectra within the algebraic framework.

Insights into how these spectra relate to classical spectral concepts.

Abstract

In this paper we consider shift operators, self-adjoint, unitary and normal operators on the standard module over a unital C*-algebra A. We define various generalized spectra in A of these operators, give description of such spectra of these operators and investigate their further properties.