On some invariant subspaces
Yoshiki Ohno · Proceedings of the Japan Academy Series A Mathematical Sciences · 1970
Let X be a compact Hausdorff space and let A be a function algebra on X.Throughout this paper, will be a fixed multiplicative linear functional on A which admits a unique representing measure m.Further we assume that the Gleason part of is non trivial.We denote by A0 the maximal ideal associated with A0--{f e A" (f)-0}.Let H2:-H2(dm) be the closure [A]2 of A in L2-L(dm).We put H=(fH;fdm-O}.We shall refer to Browder [1] for the abstract function theory in this situation.Let M be a closed subspace of H. M is called simply invariant if [AoM]2+M.We call M complementary invariant if H@M, the orthogonal complement of M in H , is simply invariant.The purpose of this paper is a characterization of the complementary invariant subspace.