Positive-operator-valued measures

A general setting for frames

Bill Moran, Stephen Howard, Douglas Cochran

Research output: Chapter in Book/Report/Conference proceedingChapter

7 Citations (Scopus)

Abstract

This chapter presents an overview of close parallels that exist between the theory of positive-operator-valued measures (POVMs) associated with a separable Hilbert space and the theory of frames on that space, including its most important generalizations. The concept of a framed POVM is introduced, and classical frames, fusion frames, generalized frames, and other variants of frames are all shown to arise as framed POVMs. This observation allows drawing on a rich existing theory of POVMs to provide new perspectives in the study of frames.

Original languageEnglish (US)
Title of host publicationApplied and Numerical Harmonic Analysis
PublisherSpringer International Publishing
Pages49-64
Number of pages16
Edition9780817683788
DOIs
StatePublished - Jan 1 2013

Publication series

NameApplied and Numerical Harmonic Analysis
Number9780817683788
ISSN (Print)2296-5009
ISSN (Electronic)2296-5017

Fingerprint

Hilbert spaces
Positive Operator
Fusion reactions
Separable Hilbert Space
Fusion

Keywords

  • Frame
  • Framed POVM
  • Fusion frame
  • Generalized frame
  • Naimark’s Theorem
  • Positive operator-valued measure(POVM)
  • Radon-Nikodym Theorem
  • Spectral measure
  • Stinespring’s Theorem

ASJC Scopus subject areas

  • Applied Mathematics

Cite this

Moran, B., Howard, S., & Cochran, D. (2013). Positive-operator-valued measures: A general setting for frames. In Applied and Numerical Harmonic Analysis (9780817683788 ed., pp. 49-64). (Applied and Numerical Harmonic Analysis; No. 9780817683788). Springer International Publishing. https://doi.org/10.1007/978-0-8176-8379-5_4

Positive-operator-valued measures : A general setting for frames. / Moran, Bill; Howard, Stephen; Cochran, Douglas.

Applied and Numerical Harmonic Analysis. 9780817683788. ed. Springer International Publishing, 2013. p. 49-64 (Applied and Numerical Harmonic Analysis; No. 9780817683788).

Research output: Chapter in Book/Report/Conference proceedingChapter

Moran, B, Howard, S & Cochran, D 2013, Positive-operator-valued measures: A general setting for frames. in Applied and Numerical Harmonic Analysis. 9780817683788 edn, Applied and Numerical Harmonic Analysis, no. 9780817683788, Springer International Publishing, pp. 49-64. https://doi.org/10.1007/978-0-8176-8379-5_4
Moran B, Howard S, Cochran D. Positive-operator-valued measures: A general setting for frames. In Applied and Numerical Harmonic Analysis. 9780817683788 ed. Springer International Publishing. 2013. p. 49-64. (Applied and Numerical Harmonic Analysis; 9780817683788). https://doi.org/10.1007/978-0-8176-8379-5_4
Moran, Bill ; Howard, Stephen ; Cochran, Douglas. / Positive-operator-valued measures : A general setting for frames. Applied and Numerical Harmonic Analysis. 9780817683788. ed. Springer International Publishing, 2013. pp. 49-64 (Applied and Numerical Harmonic Analysis; 9780817683788).
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