Maximality of Positive Operator-valued Measures

Maximality of Positive Operator-valued Measures A positive operator-valued measure is a (weak-star) countably additive set function from a σ-field Σ to the space of nonnegative bounded operators on a separable complex Hilbert space [InlineMediaObject not available: see fulltext.]. Such functions can be written as M = V*E(·)V in which E is a spectral measure acting on a complex Hilbert space [InlineMediaObject not available: see fulltext.] and V is a bounded operator from [InlineMediaObject not available: see fulltext.] to [InlineMediaObject not available: see fulltext.] such that the only closed linear subspace of [InlineMediaObject not available: see fulltext.], containing the range of V and reducing E (Σ), is [InlineMediaObject not available: see fulltext.] itself. Attention is paid to an existing notion of maximality for positive operator-valued measures. The purpose of this paper is to show that M is maximal if and only if E, in the above representation of M, generates a maximal commutative von Neumann algebra. Positivity Springer Journals

Maximality of Positive Operator-valued Measures

Loading next page...
Copyright © 2006 by Birkhäuser Verlag, Basel
Mathematics; Fourier Analysis; Operator Theory; Potential Theory; Calculus of Variations and Optimal Control; Optimization; Econometrics
Publisher site
See Article on Publisher Site


You’re reading a free preview. Subscribe to read the entire article.

DeepDyve is your
personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

Enjoy affordable access to
over 12 million articles from more than
10,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

Unlimited reading

Read as many articles as you need. Full articles with original layout, charts and figures. Read online, from anywhere.

Stay up to date

Keep up with your field with Personalized Recommendations and Follow Journals to get automatic updates.

Organize your research

It’s easy to organize your research with our built-in tools.

Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

See the journals in your area

Monthly Plan

  • Read unlimited articles
  • Personalized recommendations
  • No expiration
  • Print 20 pages per month
  • 20% off on PDF purchases
  • Organize your research
  • Get updates on your journals and topic searches


Start Free Trial

14-day Free Trial

Best Deal — 39% off

Annual Plan

  • All the features of the Professional Plan, but for 39% off!
  • Billed annually
  • No expiration
  • For the normal price of 10 articles elsewhere, you get one full year of unlimited access to articles.



billed annually
Start Free Trial

14-day Free Trial