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Among them an operator valued distribution supported by the spectrum has a distinguished position.
In this talk, I will introduce a class of independence relations which include free, Boolean and monotone independence in operator valued probability.
We introduce generalized operator valued Jost solutions of first order ill-posed differential equations on Hilbert spaces.
J. Bourgain, F.A. Grünbaum, L. Velázquez and J. Wilkening; Quantum recurrence of a subspace and operator valued Schur functions, (on line already) in Comm.
Conditions are given which guarantee the boundedness of the operator valued set function associated with a semigroup and a spectral measure.
In technical language, this is a measurement associated with a POVM (positive operator valued measure).
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We characterize operator-valued Bergman inner functions on the unit ball as functions admitting a suitable transfer function realization.
This procedure leads to operator-valued distributions instead of operator-valued fields.
I will briefly review some analytic properties of operator-valued free, Boolean and monotone convolutions.
A lifting property for subordinated invariant kernels is proved and extended to operator-valued kernels.
We also obtain Pick Julia theorems for free holomorphic functions with operator-valued coefficients.
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