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
Published: Jan 1, 2005
It’s your single place to instantly
discover and read the research
that matters to you.
Enjoy affordable access to
over 18 million articles from more than
15,000 peer-reviewed journals.
All for just $49/month
Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly
Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.
Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals.
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.
“Hi guys, I cannot tell you how much I love this resource. Incredible. I really believe you've hit the nail on the head with this site in regards to solving the research-purchase issue.”Daniel C.
“Whoa! It’s like Spotify but for academic articles.”@Phil_Robichaud
“I must say, @deepdyve is a fabulous solution to the independent researcher's problem of #access to #information.”@deepthiw
“My last article couldn't be possible without the platform @deepdyve that makes journal papers cheaper.”@JoseServera