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)
Operator-valued inner product and operator inequalities. (English) Zbl 1151.47024

For a Hilbert space H, the C * -inner product 𝐘 * 𝐗= j=1 n Y j * X j (𝐗=(X j ), 𝐘=(Y j )B(H,H n )) makes B(H,H n ) into a Hilbert C * -module over B(H). Using this operator-valued inner product, the author of present paper nicely presents operator versions for the Schwarz and Jensen inequalities and gives simple conditions that the equalities hold. Among his results, we mention the following version of the Schwarz inequality: for operators X and Y acting on a Hilbert space, the inequality

Y * X * YX+X * Y * XY(XY) * XY+(YX) * YX

holds with equality only when X commutes with Y.

47A63Operator inequalities
47A75Eigenvalue problems (linear operators)
47A80Tensor products of operators
47A56Functions whose values are linear operators