Improper filtrations for C*-algebras: spectra of unilateral tridiagonal operators

TL;DR

This paper explores the spectral properties of unilateral tridiagonal operators within C*-algebras, extending previous work to new operator classes and analyzing their algebraic structures.

Contribution

It introduces an extension of earlier results to unilateral sections, revealing new spectral analysis techniques for non-Toeplitz operators in C*-algebras.

Findings

Established a short exact sequence for the operator algebra

Connected spectral properties to algebraic extensions

Compared unilateral operators to Toeplitz operators on Hardy spaces

Abstract

We extend the results of our previous paper "C*-algebras and numerical linear algebra" to cover the case of "unilateral" sections. This situation bears a close resemblance to the case of Toeplitz operators on Hardy spaces, in spite of the fact that the operators here are far from Toeplitz operators. In particular, there is a short exact sequence 0 --> K --> A --> B --> 0 whose properties are essential to the problem of computing the spectra of self adjoint operators.