It is shown that for any (n + 1)-positive (possibly non-linear) map Φ and any bounded linear operators A i ,i = 1,¨,n we have [Φ(A i * A j )] i,j = 1 *≥[Φ(A i )*Φ(A j )] i,j = 1 *, and that the statement is false if "(n + 1)-positive" is replaced by "n-positive". This resolves an issue raised by Bhatia and Davis in relation to a Schwartz inequality which can be regarded as a non-commutative variance-covariance inequality 
Positivity – Springer Journals
Published: Oct 21, 2004
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