Spectral scale of selfadjoint operators and trace inequalities

DOI10.1016/0022-247X(85)90176-3zbMath0655.47032MaRDI QIDQ1109317

Dénes Petz

Publication date: 1985

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

zbMATH Keywords

concavitytracedensity matrixC *-algebras with a tracial stateentropy of a stategeneralized singular valuesspectral scale of a selfadjoint element in a finite von Neumanntracial positive linear maps

Mathematics Subject Classification ID

Free probability and free operator algebras (46L54) Linear operators belonging to operator ideals (nuclear, (p)-summing, in the Schatten-von Neumann classes, etc.) (47B10) General theory of (C^*)-algebras (46L05) Noncommutative probability and statistics (46L53) Noncommutative measure and integration (46L51) Linear operators in (C^*)- or von Neumann algebras (47C15)

Related Items (25)

Majorizations for generalized s-numbers in semifinite von Neumann algebras ⋮ Quasi-entropies for finite quantum systems ⋮ A contractive version of a Schur-Horn theorem in \(\mathrm{II}_{1}\) factors ⋮ Trace norm convergence of exponential product formula ⋮ Non-commutative Banach function spaces ⋮ Characterizations of the trace ⋮ Norm inequalities for the spectral spread of Hermitian operators ⋮ Lieb type convexity for positive operator monotone decreasing functions ⋮ Norms of skew-adjoint derivations with values in the predual of a semifinite von Neumann algebra ⋮ Closed convex hulls of unitary orbits in \(C^{\ast}\)-algebras of real rank zero ⋮ Numerical Ranges in II₁ Factors ⋮ Extension of spectral scales to unbounded operators ⋮ The carpenter and Schur-Horn problems for masas in finite factors ⋮ Closed Convex Hulls of Unitary Orbits in von Neumann Algebras ⋮ Alberti-Uhlmann problem on Hardy-Littlewood-Pólya majorization ⋮ Klyachko's theorem in semi-finite von Neumann algebras ⋮ Closed convex hulls of unitary orbits in \({C^{\ast}_{r}(\mathbb{F}_{\infty})}\) ⋮ Operator differentiable functions ⋮ Homogeneous manifolds from noncommutative measure spaces ⋮ CONVEX MULTIVARIABLE TRACE FUNCTIONS ⋮ Extreme points of the set of elements majorised by an integrable function: resolution of a problem by Luxemburg and of its noncommutative counterpart ⋮ Thompson’s theorem for $II_1$ factors ⋮ Jensen's Trace Inequality in Several Variables ⋮ Anti-norms on finite von Neumann algebras ⋮ Majorizations and inequalities in matrix theory

Cites Work

• Representations of uniformly hyperfinite algebras and their associated von Neumann rings
• Tracial Positive Linear Maps of C ∗ -Algebras
• Interpolation zwischen den Klassen 𝔖_p von Operatoren in Hilberträumen
• Theory of operator algebras I.
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