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Semisimplicity and global dimension of a finite von Neumann algebra

Lia Vaš (2007)

Mathematica Bohemica

We prove that a finite von Neumann algebra 𝒜 is semisimple if the algebra of affiliated operators 𝒰 of 𝒜 is semisimple. When 𝒜 is not semisimple, we give the upper and lower bounds for the global dimensions of 𝒜 and 𝒰 . This last result requires the use of the Continuum Hypothesis.

Spectral isometries

Martin Mathieu (2005)

Banach Center Publications

In this survey, we summarise some of the recent progress on the structure of spectral isometries between C*-algebras.

Stabilité du comportement des marches aléatoires sur un groupe localement compact

Driss Gretete (2008)

Annales de l'I.H.P. Probabilités et statistiques

Dans cet article nous démontrons un théorème de stabilité des probabilités de retour sur un groupe localement compact unimodulaire, séparable et compactement engendré. Nous démontrons que le comportement asymptotique de F*(2n)(e) ne dépend pas de la densité F sous des hypothèses naturelles. A titre d’exemple nous établissons que la probabilité de retour sur une large classe de groupes résolubles se comporte comme exp(−n1/3).

Subharmonicity in von Neumann algebras

Thomas Ransford, Michel Valley (2005)

Studia Mathematica

Let ℳ be a von Neumann algebra with unit 1 . 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 - 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 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.

Sums of commutators in ideals and modules of type II factors

Kenneth J. Dykema, Nigel J. Kalton (2005)

Annales de l’institut Fourier

Let be a factor of type II or II 1 having separable predual and let ¯ be the algebra of affiliated τ -measurable operators. We characterize the commutator space [ , 𝒥 ] for sub- ( , ) - bimodules and 𝒥 of ¯ .

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