Geodesic
Models for joint isometries
Glasgow mathematical journal, Tome 38 (1996) no. 2, pp. 191-194

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

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]. 
Attele, K. R. M.; Lubin, A. R. Models for joint isometries. Glasgow mathematical journal, Tome 38 (1996) no. 2, pp. 191-194. doi: 10.1017/S0017089500031426
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[1] 1.Athavale, A., On the intertwining of joint isometries, J. Operator Theory 23 (1990), 339–350. Google Scholar

[2] 2.Jewell, N. P. and Lubin, A. R., Commuting weighted shifts and analytic function theory of several variables, J. Operator Theory 1 (1979), 207–223. Google Scholar

[3] 3.Lubin, A. R., Models for commuting contractions, Michigan Math. J. 23 (1976), 161–165. Google Scholar | DOI

[4] 4.Lubin, A. R. and Attele, K. R. M., Dilations and commutant lifting for jointly-isometric operators—a geometric approach, to appear in J. Func. Anal. Google Scholar

[5] 5.Müller, V. and Vasilescu, F.-H., Standard models for some commuting multioperators, Proc. Amer. Math. Soc. 117 (1993), 979–989. Google Scholar | DOI

[6] 6.Vasilescu, F.-H., An operator valued Poisson kernel, J. Func. Anal. 110 (1992), 47–72. Google Scholar | DOI

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