Abstract
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 $bv_p (1<p<\infty)$.
Highlights
We discuss about the point spectrum, continuous spectrum, residual spectrum, approximate point spectrum, defect spectrum and compression spectrum
(iii) The residual spectrum σr(T, X) is the set of complex numbers α such that Tα−1 exists but not satisfy (R3), that is, the domain of Tα−1 is not dense in X. This is to note that in finite dimensional case, continuous spectrum coincides with the residual spectrum and equal to the empty set and the spectrum consists of only the point spectrum
Tripathy and Paul [17] studied the spectrum of the operator B(f, g) on the vector valued sequence space c0(X)
Summary
We discuss about the point spectrum, continuous spectrum, residual spectrum, approximate point spectrum, defect spectrum and compression spectrum. Tripathy and Paul ([16],[18],[19]) studied the spectra of the difference type operators D(r, 0, 0, s) and D(r, 0, s, 0, t) over the sequence spaces c0, c, lp and bvp. Paul and Tripathy ([11],[13]) have investigated the fine spectra of the operator D(r, 0, 0, s) over the sequence spaces lp, bvp and bv0 respectively.
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