The pseudospectrum of a 2×2 block matrices of sequences of linear
operators converging in the generalized sens
Abstract
trix Mn = An Cn Dn Bn , where An,Bn are two sequences of closed linear
operators and Cn,Dn are assumed to be sequences of bounded linear
operators acting in X. In the present paper, we determine the conditions
under which we have Mn converges in the generalized sense. The primary
question which has
attractedourattentioniswhetherornotthereexistsarelationshipbetween the
Weyl essential pseudospectrum of Mn converging in the generalized sense
and that of its limit.