zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
More operator versions of the Schwarz inequality. (English) Zbl 0984.46040
Let $B(H)$ be the space of all bounded linear operators on a complex separable Hilbert space $H$. Let $\Phi$ be a unital completely positive map on $B(H)$. Define $cov(A,B)=\Phi(A^*B)-\Phi(A)^*\Phi(B)$, $A,B\in B(H)$. The following generalization of the Schwarz inequality is proved: for any $A_1,A_2\in B(H)$ the block matrix $(cov(A_i,A_j)_{i,j=1}^{2}$ is positive. An operator version of the well-known Wielandt inequality is proved. The proof uses an operator version of Kantarovich inequality, which was proved by the authors in [Am. Math. Monthly 107, 353-356 (2000; Zbl 1009.15009)].

46L53Noncommutative probability and statistics
47A63Operator inequalities
60E15Inequalities in probability theory; stochastic orderings
81S25Quantum stochastic calculus
60H05Stochastic integrals
Full Text: DOI