Vol. 41, No. 1, 1972

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Strong concentration of the spectra of self-adjoint operators

Chris Rorres

Vol. 41 (1972), No. 1, 237–246

Let H be a self-adjoint operator with spectral measure E(S) over the Borel sets S of the real line. The spectrum of H is said to be strongly concentrated on S if whenever Hn converges strongly to H in the generalized sense it is true that En(S) converges strongly to the identity. Sufficient conditions on H are given for this to occur for a given arbitrary Borel set S and necessary and sufficient conditions when S is the spectrum of H. In addition several more workable sufficient conditions are cited and a few examples illustrating the results are given.

Mathematical Subject Classification 2000
Primary: 47A55
Received: 23 July 1970
Published: 1 April 1972
Chris Rorres