The Szegő infimum
HTML articles powered by AMS MathViewer
- by Berrien Moore PDF
- Proc. Amer. Math. Soc. 29 (1971), 55-62 Request permission
Erratum: Proc. Amer. Math. Soc. 31 (1972), 638-638.
Abstract:
This paper studies the Szegö infimum relative to a nonnegative, essentially bounded, operator-valued weight function and obtains a necessary and sufficient condition for this infimum to be positive.References
- Arlen Brown and P. R. Halmos, Algebraic properties of Toeplitz operators, J. Reine Angew. Math. 213 (1963/64), 89–102. MR 160136, DOI 10.1007/978-1-4613-8208-9_{1}9
- Allen Devinatz, The factorization of operator valued functions, Ann. of Math. (2) 73 (1961), 458–495. MR 126702, DOI 10.2307/1970313
- R. G. Douglas, On factoring positive operator functions, J. Math. Mech. 16 (1966), 119–126. MR 0209887, DOI 10.1512/iumj.1967.16.16007
- Paul R. Halmos, Shifts on Hilbert spaces, J. Reine Angew. Math. 208 (1961), 102–112. MR 152896, DOI 10.1515/crll.1961.208.102
- Henry Helson, Lectures on invariant subspaces, Academic Press, New York-London, 1964. MR 0171178
- Henry Helson and David Lowdenslager, Prediction theory and Fourier series in several variables, Acta Math. 99 (1958), 165–202. MR 97688, DOI 10.1007/BF02392425
- Magnus R. Hestenes, Relative self-adjoint operators in Hilbert space, Pacific J. Math. 11 (1961), 1315–1357. MR 136996
- Kenneth Hoffman, Banach spaces of analytic functions, Prentice-Hall Series in Modern Analysis, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1962. MR 0133008
- Edward M. Landesman, Hilbert-space methods in elliptic partial differential equations, Pacific J. Math. 21 (1967), 113–131. MR 209911
- David B. Lowdenslager, On factoring matrix valued functions, Ann. of Math. (2) 78 (1963), 450–454. MR 155154, DOI 10.2307/1970535
- N. Wiener and P. Masani, The prediction theory of multivariate stochastic processes. II. The linear predictor, Acta Math. 99 (1958), 93–137. MR 97859, DOI 10.1007/BF02392423
- Berrien Moore III, A factorable weight with zero Szegö infimum, Proc. Amer. Math. Soc. 35 (1972), 301–302. MR 322573, DOI 10.1090/S0002-9939-1972-0322573-2
- Marvin Rosenblum, Self-adjoint Toeplitz operators and associated orthonormal functions, Proc. Amer. Math. Soc. 13 (1962), 590–595. MR 138001, DOI 10.1090/S0002-9939-1962-0138001-X
- Marvin Rosenblum, Vectorial Toeplitz operators and the Fejér-Riesz theorem, J. Math. Anal. Appl. 23 (1968), 139–147. MR 227794, DOI 10.1016/0022-247X(68)90122-4 B. Sz.-Nagy and C. Foias, Analyse harmonique des opérateurs de l’espace de Hilbert, Masson, Paris; Akad. Kiadó, Budapest, 1967. MR 37 #778.
- G. Szegő, Beiträge zur Theorie der Toeplitzschen Formen, Math. Z. 6 (1920), no. 3-4, 167–202 (German). MR 1544404, DOI 10.1007/BF01199955
Additional Information
- © Copyright 1971 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 29 (1971), 55-62
- MSC: Primary 47.40
- DOI: https://doi.org/10.1090/S0002-9939-1971-0290170-2
- MathSciNet review: 0290170