Subharmonicity in von Neumann algebras

Thomas Ransford; Michel Valley

Studia Mathematica, Tome 166 (2005), p. 219-226 / Harvested from The Polish Digital Mathematics Library

Résumé

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 $μ_{t} {(x)}_{t \geq 0}$ 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, $λ \mapsto \int_{0}^{t} l o g μ_{s} (f (λ)) d s$ is a subharmonic function on D. This generalizes earlier subharmonicity results of White and Aupetit on the singular values of matrices.

Publié le : 2005-01-01

Zbl 1095.46035

EUDML-ID : urn:eudml:doc:284793

@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm170-3-1,
     author = {Thomas Ransford and Michel Valley},
     title = {Subharmonicity in von Neumann algebras},
     journal = {Studia Mathematica},
     volume = {166},
     year = {2005},
     pages = {219-226},
     zbl = {1095.46035},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm170-3-1}
}

Thomas Ransford; Michel Valley. Subharmonicity in von Neumann algebras. Studia Mathematica, Tome 166 (2005) pp. 219-226. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm170-3-1/