Complementary Inequalities III: Inequalities Complementary to Schwarz’s Inequality in Hilbert Space

J. B. Diaz and F. T. Metcalf

A chapter in Contributions to Functional Analysis, 1966, pp 120-139 from Springer

Abstract: Abstract The Schwarz inequality [18, p. 198] in a Hilbert space (with real or complex scalars) implies that % MathType!MTEF!2!1!+- % feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBamXvP5wqonvsaeHbd9wDYLwzYbqe % e0evGueE0jxyaibaieYlf9irVeeu0dXdh9vqqj-hEeeu0xXdbba9fr % Fj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs0dXdbPYx % e9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaa % aaaaaapeGaaiiFamaabmaapaqaa8qacaWGbbGaamiEaiaacYcapaGa % aG5bV-qacaWGcbGaamiEaaGaayjkaiaawMcaaiaacYhapaWaaWbaaS % qabeaapeGaaGOmaaaakiqbgYda8yaaDyaaDaWdaiaayEW7peWaaeWa % a8aabaWdbiaadgeacaWG4bGaaiila8aacaaMh8+dbiaadgeacaWG4b % aacaGLOaGaayzkaaWdaiaayEW7peWaaeWaa8aabaWdbiaadkeacaWG % 4bGaaiila8aacaaMh8+dbiaadkeacaWG4baacaGLOaGaayzkaaGaai % ilaaaa!564C! $$|\left( {Ax,{\mkern 1mu} Bx} \right){|^2}\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}\to {\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}\to {

Keywords: Hilbert Space; Equality Condition; Null Space; Schwarz Inequality; Equality Sign (search for similar items in EconPapers)
Date: 1966
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-85997-7_5

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DOI: 10.1007/978-3-642-85997-7_5

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