Subharmonicity in von Neumann algebras

• Autorzy: Thomas Ransford , Michel Valley
• Języki publikacji: EN

Abstrakty

EN

Let ℳ be a von Neumann algebra with unit $1_{ℳ}$. Let τ be a faithful, normal, semifinite trace on ℳ. Given x ∈ ℳ, denote by $μ_{t}(x)_{t≥0}$ the generalized s-numbers of x, defined by
$μ_{t}(x)$ = inf{||xe||: e is a projection in ℳ i with $τ(1_{ℳ} - e)$ ≤ t} (t ≥ 0).
We prove that, if D is a complex domain and f:D → ℳ is a holomorphic function, then, for each t ≥ 0, $λ ↦ ∫_{0}^{t} log μ_{s} (f(λ))ds$ is a subharmonic function on D. This generalizes earlier subharmonicity results of White and Aupetit on the singular values of matrices.

Kategorie tematyczne

• 31A05: Harmonic, subharmonic, superharmonic functions
• 15A18: Eigenvalues, singular values, and eigenvectors
• 46L10: General theory of von Neumann algebras

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2005
• Tom: 170
• Numer: 3
• Strony: 219-226

Daty

wydano

2005

Twórcy

autor

Thomas Ransford

• Département de mathématiques et de statistique, Université Laval, Québec (QC), Canada G1K 7P4

autor

Michel Valley

• Département de mathématiques et de statistique, Université Laval, Québec (QC), Canada G1K 7P4

Identyfikatory

DOI

10.4064/sm170-3-1