Toeplitz operators associated with isometries

Moore, B.; Rosenblum, M.; Rovnyak, J.

doi:10.1090/S0002-9939-1975-0374978-4

Toeplitz operators associated with isometries
HTML articles powered by AMS MathViewer

by B. Moore, M. Rosenblum and J. Rovnyak PDF

Proc. Amer. Math. Soc. 49 (1975), 189-194 Request permission

Abstract:

Shift analysis includes abstract treatments of inner-outer factorization problems, the factorization problem for nonnegative functions on a circle, and Szegö’s infimum problem (for scalar or operator valued functions). These problems are here generalized to a setting where the shift operator is replaced by a pair of isometries.

References

Allen Devinatz and Marvin Shinbrot, General Wiener-Hopf operators, Trans. Amer. Math. Soc. 145 (1969), 467–494. MR 251573, DOI 10.1090/S0002-9947-1969-0251573-0
R. G. Douglas, On the operator equation $S^{\ast } XT=X$ and related topics, Acta Sci. Math. (Szeged) 30 (1969), 19–32. MR 250106
Berrien Moore III, The Szegő infimum, Proc. Amer. Math. Soc. 29 (1971), 55–62. MR 290170, DOI 10.1090/S0002-9939-1971-0290170-2
Paul S. Muhly, Inner functions and isometries, Canad. Math. Bull. 18 (1975), no. 3, 383–385. MR 397466, DOI 10.4153/CMB-1975-070-3
Lavon B. Page, Applications of the Sz.-Nagy and Foiaş lifting theorem, Indiana Univ. Math. J. 20 (1970/71), 135–145. MR 261388, DOI 10.1512/iumj.1970.20.20013

Factoring in the commutant of a normal operator

Marvin Rosenblum and James Rovnyak, The factorization problem for nonnegative operator valued functions, Bull. Amer. Math. Soc. 77 (1971), 287–318. MR 273437, DOI 10.1090/S0002-9904-1971-12671-X