01-155 R. Killip, C. Remling

Reducing Subspaces (28K, LaTeX) Apr 25, 01

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Abstract. Let $T$ be a self-adjoint operator acting in a separable Hilbert space. We establish a correspondence between the reducing subspaces of $T$ that come from a spectral projection and the convex, norm-closed bands in the set of finite Borel measures on $R$. If the Hilbert space is not separable, we still obtain a reducing subspace corresponding to each convex norm-closed band. These observations lead to a unified treatment of various reducing subspaces. Moreover, they also settle some open questions and suggest new decompositions.

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