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Operators on Hilbert Space

  • 2016
  • Buch

Über dieses Buch

The primarily objective of the book is to serve as a primer on the theory of bounded linear operators on separable Hilbert space. The book presents the spectral theorem as a statement on the existence of a unique continuous and measurable functional calculus. It discusses a proof without digressing into a course on the Gelfand theory of commutative Banach algebras. The book also introduces the reader to the basic facts concerning the various von Neumann–Schatten ideals, the compact operators, the trace-class operators and all bounded operators.

Inhaltsverzeichnis

  1. Frontmatter

  2. Chapter 1. Hilbert space

    V. S. Sunder
    Abstract
    This book is about (bounded, linear) operators on (always separable and com-plex) Hilbert spaces, usually denoted by ℋ, K, ℳ and variants thereof. Vectors in Hilbert spaces will usually be denoted by symbols such as x, y, z and their variants, such as yn, x′.
  3. Chapter 2. The Spectral Theorem

    V. S. Sunder
    Abstract
    It will be convenient, indeed desirable, to use the language of C*-algebras.
  4. Chapter 3. Beyond normal operators

    V. S. Sunder
    Abstract
    In this section, we establish the very useful polar decomposition for bounded operators on Hilbert space. We begin with a few simple observations and then introduce the crucial notion of a partial isometry.
  5. Backmatter

Titel
Operators on Hilbert Space
Verfasst von
V. S. Sunder
Copyright-Jahr
2016
Verlag
Springer Singapore
Electronic ISBN
978-981-10-1816-9
Print ISBN
978-981-10-1816-9
DOI
https://doi.org/10.1007/978-981-10-1816-9

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