the main purpose of this paper is to detemine the fine spectrum of the generalized difference operator delta_{uv} over the sequence space c0. these results are more general than the fine spectrum of the generalized difference operator delta_{uv} of srivastava and kumar.

We present new generalized Jacobson?s lemma for Drazin inverses. This extends the main results on g-Drazin inverse of Yan, Zeng and Zhu (Linear & Multilinear Algebra, 68(2020), 81-93).

We consider the curvatures 2 form asociated with AdSL4 valued one-form gauge connetion, and then we construct a four-dimensional action that generalize Einstein-Hilbert gravity. It is shown Maxwell extension of Einstein gravity can be obtained from AdSL4-gravity making use Inonu-Wigner contraction method. In same way, by gauging AdSL5 spacetime algebra, extended including vector fields kab ha w...