Complements to models for noncommuting operators
This paper of A. E. Frazho develops a dilation theory for two noncommuting operators, which can in fact be extended to the n-operator case. This is accomplished by first extending the so-called Schäffer construction [cf. \textit{J. J. Schäffer}, Proc. Am. Math. Soc. 6, 322 (1955; Zbl 0064.116) or the book ''Harmonic analysis on operators on Hilbert space'' (1967; Zbl 0157.432) by \textit{B. Sz.-Nagy} and \textit{C. Foias}] for one operator to the Fock space setting. This is then combined with a new Wold decomposition to extend the Sz.-Nagy-Foias lifting theorem and also to extend the characteristic function theory. This work is related to work of \textit{J. W. Bunce} [viz., Models for N-tuples of noncommuting operators, J. Funct. Anal. 57, 21-30 (1984; Zbl 0558.47004)].
dilation theory for two noncommuting operators
scientific article; zbMATH DE number 3929749
scientific article