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- W4247798612 abstract "A certain class of matrix-valued Borel matrix functions is introduced. It is shown that all functions of that class naturally operate on any operator T in a finite type I von Neumann algebra M in a way such that uniformly bounded sequences f1, f2,… of functions that converge pointwise to 0 transform into sequences f1[T], f2[T],… of operators in T that converge to 0 in the *-strong operator topology. It is also demonstrated that the double *-commutant of any such operator T that acts on a separable Hilbert space coincides with the set of all operators of the form f[T] where f runs over all functions from the aforementioned class. Some conclusions are drawn concerning so-called operator-spectra of such operators and a new variation of the spectral theorem is formulated." @default.
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- W4247798612 date "2016-01-01" @default.
- W4247798612 modified "2023-10-17" @default.
- W4247798612 title "Non-commutative functional calculus in finite type I von Neumann algebras" @default.
- W4247798612 doi "https://doi.org/10.1353/mpr.2016.0009" @default.
- W4247798612 hasPublicationYear "2016" @default.
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