Abstract
In this paper we have examined the approximate point spectrum, defect spectrum and compression spectrum of the operator D(r, 0, 0, s)on the sequence spaces c0, c, ℓp and bvp.
Highlights
Subdivisions of the spectrumWe discuss about the point spectrum, continuous spectrum, residual spectrum, approximate point spectrum, defect spectrum and compression spectrum
The resolvent set of T is the set of all such regular values α of T, denoted by ρ(T )
We discuss about the point spectrum, continuous spectrum, residual spectrum, approximate point spectrum, defect spectrum and compression spectrum
Summary
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 (and may be bounded or not) 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. The two subspectra given by (a) and (b) form a (not necessarily disjoint) subdivisions σ(T, X) = σap(T, X) ∪ σco(T, X) of the spectrum.
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