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Coisometric extension and functional calculus for pairs of commuting contractions. (English) Zbl 0872.47009

The purpose of this paper is twofold: on one hand we aim at presenting a (modest) extension of the functional calculus for pairs of commuting contractions constructed in [E. Briem, A. M. Davic and B. K. Øksendal, J. Lond. Math. Soc., II. Ser. 7, 709-718 (1974; Zbl 0291.47015)]. On the other hand, we are interested in studying joint coisometric extensions of pairs of commuting contractions. Related dilations have been studied by M. Slociński in [Bull. Acad. Pol. Sci., Ser. Sci. Math. Astron. Phys. 25 (1977), 1233-1242 (1978; Zbl 0384.47005)]. These two topics are not without relation and we intend to exploit this relation in this and future work.

MSC:

47A60 Functional calculus for linear operators
47A20 Dilations, extensions, compressions of linear operators
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