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Models for joint isometries

Published online by Cambridge University Press:  18 May 2009

K. R. M. Attele  and
A. R. Lubin
K. R. M. Attele
Affiliation:
Department of Mathematics, Illinois Institute of Technology, Chicago, IL 60616, U.S.A.
A. R. Lubin
Affiliation:
Department of Mathematics, Illinois Institute of Technology, Chicago, IL 60616, U.S.A.
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An N-tuple ℐ= (T1…, TN) of commuting contractions on a Hilbert space H is said to be a joint isometry if for all x in H, or, equivalently, if Athavale in [1] characterized the joint isometries as subnormal N-tuples whose minimal normal extensions have joint spectra in the unit sphere S2N−X a geometric perspective of this is given in [4]. Subsequently, V. Müller and F.-H. Vasilescu proved that commuting N-tuples which are joint contractions, i.e. , can be represented as restrictions of certain weighted shifts direct sum a joint isometry. In this paper we adapt the canonical models of [3], and also construct a new canonical model, which completes the previous descriptions by showing joint isometries are indeed restrictions of specific multivariable weighted shifts [2].

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 38 , Issue 2 , May 1996 , pp. 191 - 194
Copyright
Copyright © Glasgow Mathematical Journal Trust 1996

References

REFERENCES

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