Abstract
In this paper, we show a spectral inclusion of a dierent spectra of a C0-quasi-semigroup and its generator and precisely for ordinary, point, approximate point, residual, essential and regular spectra.
Highlights
Ould Mohamed Baba abstract: In this paper, we show a spectral inclusion of a different spectra of a C0-quasi-semigroup and its generator A(t)
We focus for ordinary spectrum, point spectrum, approximate spectrum, residual spectrum and essential spectrum
Inspired by the spectral study of C0-semigroup, in this work, we show that the spectral inclusion of different spectra for C0-quasi-semigroup and its generator
Summary
For a C0-quasi-semigroup {R(t, s)}t,s≥0 on a Banach space X, let D be the set of all x ∈ X for which the following limits exist, lim R(0, s)x − x , lim R(t, s)x − x and lim R(t − s, s)x − x s→0+ {R(t, s)}t,s≥0 is a C0-quasi-semigroup with D = D(A) and its generator for all t ≥ 0 [9, Theorems 3.1 and 3.2] Let {R(t, s)}t,s≥0 be a C0-quasi-semigroup on X with generator A(t).
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