Abstract:
In this thesis whenever, A and B are semi regular operators does not imply, in general,
that the product AB is semi regular. We do, however, give conditions under which the
above implication is valid. Moreover, we study the essential approximate point spectrum
(respectively, the essential defect spectrum) of a sequence of closed linear operators
(T_{n})_{n∈N} on Banach space X, and the essential approximate point spectrum
(respectively, the essential defect spectrum) of a linear operator T on X, where
(T_{n})_{n∈N} converges to T, in the case of convergence in generalized sense as well as in
the case of the convergence compactly. And in the last we applied some results of spectral
continuity using the v-convergence to 𝟑 × 𝟑 block operator matrix.
