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Hilbert Spaces

  • Heinz H. Bauschke
  • Patrick L. Combettes
Chapter
Part of the CMS Books in Mathematics book series (CMSBM)

Abstract

Throughout this book, \(\mathcal{H}\) is a real Hilbert space with scalar (or inner) product \(\langle \cdot | \cdot \rangle\). The associated norm is denoted by \(\parallel \cdot \parallel\) and the associated distance by d, i.e.,
$$(\forall x \in \mathcal{H}) (\forall y \in \mathcal{H}) \quad \parallel x \parallel = \sqrt {\langle x | x \rangle} \ {\rm and} \ d(x, y) = \parallel x-y \parallel.$$
(2.1)

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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Mathematics Irving K. Barber SchoolUniversity of British ColumbiaKelownaCanada
  2. 2.Laboratoire Jacques-Louis LionsUniversité Pierre et Marie Curie - Paris 6ParisFrance

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