6533b828fe1ef96bd128856e
RESEARCH PRODUCT
Clarkson-McCarthy inequalities with unitary and isometry orbits
Jean-christophe BourinEun-young Leesubject
Trace (linear algebra)010103 numerical & computational mathematics01 natural sciencesUnitary stateConvexityCombinatoricssymbols.namesakeOperator (computer programming)FOS: MathematicsDiscrete Mathematics and Combinatorics0101 mathematicsMathematicsMathematics::Functional AnalysisNumerical AnalysisAlgebra and Number TheoryMathematics::Operator Algebras010102 general mathematicsHilbert spaceUnitary matrixMathematics::Spectral TheoryFunctional Analysis (math.FA)Mathematics - Functional AnalysisIsometrysymbolsComputer Science::Programming LanguagesGeometry and Topologydescription
Abstract A refinement of a trace inequality of McCarthy establishing the uniform convexity of the Schatten p-classes for p > 2 is proved: if A , B are two n-by-n matrices, then there exists some pair of n-by-n unitary matrices U , V such that U | A + B 2 | p U ⁎ + V | A − B 2 | p V ⁎ ≤ | A | p + | B | p 2 . A similar statement holds for compact Hilbert space operators. Another improvement of McCarthy's inequality is given via the new operator parallelogramm law, | A + B | 2 ⊕ | A − B | 2 = U 0 ( | A | 2 + | B | 2 ) U 0 ⁎ + V 0 ( | A | 2 + | B | 2 ) V 0 ⁎ for some pair of 2n-by-n isometry matrices U 0 , V 0 .
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2020-04-21 | Linear Algebra and its Applications |