Fine Spectra of Symmetric Toeplitz Operators

Muhammed Altun

doi:10.1155/2012/932785

Abstract

The fine spectra of 2‐banded and 3‐banded infinite Toeplitz matrices were examined by several authors. The fine spectra of n‐banded triangular Toeplitz matrices and tridiagonal symmetric matrices were computed in the following papers: Altun, “On the fine spectra of triangular toeplitz operators” (2011) and Altun, “Fine spectra of tridiagonal symmetric matrices” (2011). Here, we generalize those results to the (2n + 1)‐banded symmetric Toeplitz matrix operators for arbitrary positive integer n.

Highlights

Introduction and PreliminariesThe spectrum of an operator over a Banach space is partitioned into three parts, which are the point spectrum, the continuous spectrum, and the residual spectrum
By B X, we denote the set of all bounded linear operators on X into itself
If X is any Banach space and T ∈ B X the adjoint T ∗ of T is a bounded linear operator on the dual X∗ of X defined by T ∗φxφTx for all φ ∈ X∗ and x ∈ X

Summary

Introduction

Introduction and PreliminariesThe spectrum of an operator over a Banach space is partitioned into three parts, which are the point spectrum, the continuous spectrum, and the residual spectrum. By B X , we denote the set of all bounded linear operators on X into itself. If X is any Banach space and T ∈ B X the adjoint T ∗ of T is a bounded linear operator on the dual X∗ of X defined by T ∗φxφTx for all φ ∈ X∗ and x ∈ X.

Results

Conclusion