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A variational problem in Hilbert space |
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| Authors: | J. Ernest Wilkins Jr. |
| Affiliation: | 1. Howard University, Washington, D.C., USA |
| Abstract: | Let? be a Hilbert space over the field of complex numbers, with inner product (g,h). Letf be a fixed element in?, and letH be a compact, self-adjoint linear operator on?. We find the maximum value ofQ f (u)=|(f,u)|2 in the classU of elementsu in? for which (u,u)=1, (u, Hu)=0. |
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