Vol. 37, No. 2, 1971

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An approximation theory for elliptic quadratic forms on Hilbert spaces: Application to the eigenvalue problem for compact quadratic forms

John Gregory

Vol. 37 (1971), No. 2, 383–395

A theory for an elliptic quadratic form J(x) defined on a Hilbert space A has been given by Hestenes. A fundamental part of this theory is concerned with the signature s and nullity n of J(χ) on A. These indices are used to develop a generalized Sturm-Lionville Theory and a Local Morse Theory. In this paper the theory of Hestenes is extended to elliptic quadratic forms J(x;σ) defined on A(σ) where σ is a member of the metric space ,|0) and A(σ) denotes a closed subspace of A. A fundamental part of this extension is concerned with inequalities dealing with the signature s(σ) and nullity n(σ) of J(x;σ) on A(σ), where σ is in a ρ neighborhood of a fixed point σ0 in Σ.

Mathematical Subject Classification
Primary: 46N05
Secondary: 49G99
Received: 10 April 1970
Revised: 10 August 1970
Published: 1 May 1971
John Gregory