Geodesic
Von Neumann Operators in
Canadian mathematical bulletin, Tome 27 (1984) no. 2, pp. 146-156

Voir la notice de l'article provenant de la source Cambridge University Press

For a connected open subset Ω of the plane and n a positive integer, let be the space introduced by Cowen and Douglas in their paper, “Complex geometry and operator theory”. Our main concern is the case n = 1, in which case we show the existence of a functional calculus for von Neumann operators in for which a spectral mapping theorem holds. In particular we prove that if the spectrum of , is a spectral set for T, and if , then σ(f(T)) = f(Ω)- for every bounded analytic function f on the interior of L, where L is compact, σ(T) ⊂ L, the interior of L is simply connected and L is minimal with respect to these properties. This functional calculus turns out to be nice in the sense that the general study of von Neumann operators in is reduced to the special situation where Ω is an open connected subset of the unit disc with .
DOI : 10.4153/CMB-1984-023-2
Mots-clés : 47B20, 47A60, 47B37, 47A2, Von Neumann operator, functional calculus, spectral set, spectral mapping 
Seddighi, Karim. Von Neumann Operators in. Canadian mathematical bulletin, Tome 27 (1984) no. 2, pp. 146-156. doi: 10.4153/CMB-1984-023-2
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