Vol. 22, No. 1, 1967

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The extension of bilinear functionals

Thomas Lee Hayden

Vol. 22 (1967), No. 1, 99–108

Using the relationship between bilinear functionals and linear operators we obtain some theorems on the extension of bilinear functionals. To extend bilinear functionals in Hilbert Spaces a special constructional process is given which is a generalization of the usual inner product. This allows the construction of bilinear functionals with special properties. In particular it allows a generalization of the Lax-Milgram Theorem. We also extend the Lax-Milgram Theorem to reflexive Banach Spaces.

Mathematical Subject Classification
Primary: 46.10
Received: 3 August 1966
Published: 1 July 1967
Thomas Lee Hayden