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

Read more

Summary

Subdivisions of the spectrum

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.

Goldberg’s classification of spectrum
Conclusion
Full Text
Published version (Free)

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call