SOME PROPERTIES OF INVARIANT SUBSPACES IN BANACH SPACES OF ANALYTIC FUNCTIONS Hedayatian, K.; Robati, B. Khani;
Let be a reflexive Banach space of functions analytic on the open unit disc and M be an invariant subspace of the multiplication operator by the independent variable, . Suppose that and : M M, defined by , is the operator of multiplication by . We would like to investigate the spectrum and the essential spectrum of and we are looking for the necessary and sufficient conditions for to be a Fredholm operator. Also we give a sufficient condition for a sequence to be an interpolating sequence for . At last the commutant of under certain conditions on M and is determined.
invariant subspaces;multiplication operators;reflexive Banach space of analytic functions;spectrum; bounded point evaluation;
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