On a characterization of the essential spectra of some matrix operators and application to two-group transport operators

In this paper, we investigate the essential approximate point spectrum and the essential defect spectrum of a 2 × 2 block operator matrix on a Banach space. Furthermore, we apply the obtained results to two-group transport operators in the Banach space L _p ([−a, a] × [−1, 1]) × L _p ([−a, a] × [−1, 1]), a > 0, p ≥ 1.     

Nonlinear representations of the group: (R +×SO(n)) ∧ R n

Nonlinear representations of the group G=(R ⁺×SO(n)) R ⁿ , such that the free part is an infinite-dimensional unitary irreducible representation of G, are proved to be formally linearizable on the space of infinitely differentiable functions with compact support.     

Essential spectra of operator matrices and applications

The main goal of this paper is to give a characterization of Wolf, Schechter, and Browder essential spectra of (2 × 2) matrix operator on a Banach space. Furthermore, we apply the obtained results to transport equations. Copyright © 2013 John Wiley & Sons, Ltd.