Vol. 81, No. 1, 1979

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Shifts on indefinite inner product spaces

Brian William McEnnis

Vol. 81 (1979), No. 1, 113–130

We use the concept of a wandering subspace to study isometries on spaces with an inner product that is not assumed to be positive definite. The theory in many respects parallels the Hilbert space theory, but there are significant differences that are emphasized here. Examples are given which illustrate the complications that can arise when the inner product is indefinite.

The first few sections of this paper are devoted to the study of indefinite inner product spaces with admissible topologies, and the continuous operators on these spaces. The rest of the paper concentrates on isometric operators, their wandering subspaces, and the Fourier representations of shifts.

Mathematical Subject Classification 2000
Primary: 47B50
Received: 10 April 1978
Published: 1 March 1979
Brian William McEnnis