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.
“…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…”
In this paper we have examined the approximate point spectrum, defect spectrum and compression spectrum of the operator D(r,0,s,0,t) on the sequence spaces c0, c, and $bv_p (1<p<\infty)$.
“…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…”
In this paper we have examined the approximate point spectrum, defect spectrum and compression spectrum of the operator D(r,0,s,0,t) on the sequence spaces c0, c, and $bv_p (1<p<\infty)$.
“…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.…”
Section: Goldberg's Classification Of Spectrummentioning
The aim of this paper is to obtain the spectrum, fine spectrum, approximate point spectrum, defect spectrum and compression spectrum of the operator U.aI 0I b/ D 2
“…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.…”
Section: Goldberg's Classification Of Spectrummentioning
The aim of this paper is to obtain the spectrum, fine spectrum, approximate point spectrum, defect spectrum and compression spectrum of the operatorSubjclass : 47A10; 47B37; 15A18.
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