Spectrum and fine spectrum of the Zweier matrix over the sequence space cs

Abstract

In this article we have determined the spectrum and fine spectrum of the Zweier matrix Zs on the sequence space cs. In a further development, we have also determined the approximate point spectrum, the defect spectrum and the compression spectrum of the operator Zs on the sequence space cs.

Subdivisions of the spectra for D(r,0,s,0,t) operator on certain sequence spaces

“…Paul and Tripathy [12] have investigated the subdivisions of the spectra for the operator D(r, 0, 0, s) over the sequence spaces c 0 , c, ℓ p and bv p . Das and Tripathy [14] studied the spectra of the lower triangular matrix B(r, s, t) over the sequence space cs and Tripathy and Das [20] studied about upper triangular matrix U (r, s) over the sequence space cs. Lemma 2.5 [17].Let s be a complex number such that √ s 2 = −s and defined the set by…”

Spectra and fine Spectra of the upper triangular band matrix U(a;0;b) over the sequence space c0

“…In [13], Tripathy and Das determined the spectra of the Rhaly operator on the class of bounded statistically null bounded variation sequence space. In [10], Paul and Tripathy investigated the so-called fine spectrum of the operator D.r; 0; 0; s/ over a sequence space bv 0 : In [3], Das and Tripathy determined the spectrum and fine spectrum of the lower triangular matrix B .r; s; t / on the sequence space cs.…”

Spectra and fine spectra for the upper triangular band matrix U(a 0 , a 1 , a 2 ; b 0 , b 1 , b 2 ) over the sequence space c 0

“…In [12], Paul and Tripathy investigated the fine spectrum of the operator D(r, 0, 0, s) over a sequence space bv 0 . In [4], the spectrum and fine spectrum of the lower triangular matrix B (r, s, t) on the sequence space cs were studied by Das and Tripathy. In [6], the fine spectrum of the lower triangular matrix B(r, s) over the Hahn sequence space was investigated by Das.…”