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Spectral Inclusion and C.N.E.

Published online by Cambridge University Press:  20 November 2018

A. R. Lubin
A. R. Lubin*
Affiliation:
Illinois Institute of Technology, Chicago, Illinois
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1. An n-tuple S = (S1, …, Sn) of commuting bounded linear operators on a Hilbert space H is said to have commuting normal extension if and only if there exists an n-tuple N = (N1, …, Nn) of commuting normal operators on some larger Hilbert space K ⊃ H with the restrictions Ni|H = Si, i = 1, …, n. If we take

the minimal reducing subspace of N containing H, then N is unique up to unitary equivalence and is called the c.n.e. of S. (Here J denotes the multi-index (j1, …, jn) of nonnegative integers and N*J = N1*jl … Nn*jn and we emphasize that c.n.e. denotes minimal commuting normal extension.) If n = 1, then S1 = S is called subnormal and N1 = N its minimal normal extension (m.n.e.).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 34 , Issue 4 , 01 August 1982 , pp. 883 - 887
Copyright
Copyright © Canadian Mathematical Society 1982

References

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