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Complex Analysis and Operator Theory

, Volume 13, Issue 3, pp 615–635 | Cite as

On Some Study of the Fine Spectra of Triangular Band Matrices

  • Arnab Patra
  • Riddhick BirbonshiEmail author
  • P. D. Srivastava
Article
  • 175 Downloads

Abstract

The present article is a continuation of the work done by Birbonshi and Srivastava (Complex Anal Oper Theory 11:739–753, 2017) where the authors obtained the spectrum and fine spectrum of banded triangular matrices such that the entries of each band are constant. In this article, we consider the same problem for triangular band matrices such that each band is a convergent sequence. These kind of matrix can be expressed as a compact perturbation of banded Toeplitz matrices. In this connection, a result regarding the location of the roots of a polynomial with respect to the unit circle is obtained. Some results on the compactnees of the operator are also derived. Finally, suitable examples are given in support of our results.

Keywords

Band matrices Spectrum of an operator Sequence spaces 

Mathematics Subject Classification

47A10 47B37 

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Department of MathematicsIndian Institute of Technology KharagpurKharagpurIndia

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