Vol. 100, No. 1, 1982

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Shifts on indefinite inner product spaces. II

Brian William McEnnis

Vol. 100 (1982), No. 1, 177–183

This paper continues the study of isometries on indefinite inner product spaces by means of their wandering subspaces. In the author’s earlier paper of the same title (Pacific J. Math., 81 (1979), 113–130), it was shown that the subspace on which an isometry acts as a shift need not be regular and that vectors in this subspace need not be recoverable from their Fourier coefficients by summation. We present here necessary and sufficient conditions for this situation not to occur, and also show that these conditions are sufficient (but not necessary) for the isometry to have a Wold decomposition.

Mathematical Subject Classification 2000
Primary: 47B50
Received: 24 September 1980
Published: 1 May 1982
Brian William McEnnis