On the spectrum of the Cesàro operator C 1 on $b\bar v_0 \cap \ell _\infty $

Abstract

ABSTRACT. In this paper we have investigated the spectrum of the Cesàro operator C 1 which is regarded as an operator on the sequence spaceb v 0 ∩ ∞ , the space of statistically null bounded variation sequences.

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

“…Also they determined the approximate point spectrum, the defect spectrum and the compression spectrum of the operator U.r; s/ on the same space. In [16], Tripathy and Saikia determined the norm and spectrum of the Cesàro matrix considered as a bounded operator on bv 0 \`1. In [15], Tripathy and Paul examined the spectra of the operator D.r; 0; 0; s/ on sequence spaces c 0 and c. In [9], Paul and Tripathy investigated the spectrum of the operator D.r; 0; 0; s/ over the sequence spaces`p and bv p .…”

Fine Spectrum of the Generalized Difference Operator B(r,s) over the Class of Convergent Series

“…We say that de�nes a matrix mapping from into , denoted by , if for every sequence the sequence { } is in , where ∑ ∞ 0 ( and ), provided the right hand side converges for every and . Spectra of some particular types of matrix operators have been investigated from different aspects by Okutoyi [1], Rhoades [2], Tripathy and Saikia [3], Tripathy and Paul [4,5], and Dutta and Tripathy [6]. Okutoyi [1] studied the spectrum of the Cesàro operator 1 on 0 .…”

The spectrum of the operator D(r,0,0,s) over the sequence space b v 0

“…Moreover, Tripathy and Paul [15] studied the spectrum of the operator ( , ) on the vector-valued sequence space 0 ( ). Some studies were also carried out by Furkan, Bilgiç and Başar [4], Rhoades [12], Tripathy and Das [13], and Tripathy and Saikia [18]. There still remains a lot to be explored on the spectra of some matrix operators transforming one class of sequences into another.…”