Bounded and compact vectorial Hankel operators
HTML articles powered by AMS MathViewer
- by Lavon B. Page PDF
- Trans. Amer. Math. Soc. 150 (1970), 529-539 Request permission
Abstract:
Operators $H$ satisfying ${S^ \ast }H = HS$ where $S$ is a unilateral shift on Hilbert space are called Hankel operators. For a fixed shift $S$ of arbitrary multiplicity the Banach spaces of bounded Hankel operators and of compact Hankel operators are described, and it is shown that the former is always the second dual of the latter. Representations for bounded and for compact Hankel operators are given in a standard function space model.References
- Paul R. Halmos, A Hilbert space problem book, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London, 1967. MR 0208368
- Philip Hartman, On completely continuous Hankel matrices, Proc. Amer. Math. Soc. 9 (1958), 862–866. MR 108684, DOI 10.1090/S0002-9939-1958-0108684-8
- Henry Helson, Lectures on invariant subspaces, Academic Press, New York-London, 1964. MR 0171178 R. N. Hevener, A functional analytic approach to Hankel and Toeplitz matrices, Thesis, Univ. of Virginia, Charlottesville, 1965.
- Kenneth Hoffman, Banach spaces of analytic functions, Prentice-Hall Series in Modern Analysis, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1962. MR 0133008
- Paul S. Muhly, Commutants containing a compact operator, Bull. Amer. Math. Soc. 75 (1969), 353–356. MR 254654, DOI 10.1090/S0002-9904-1969-12168-3
- Zeev Nehari, On bounded bilinear forms, Ann. of Math. (2) 65 (1957), 153–162. MR 82945, DOI 10.2307/1969670 M. Rosenblum, Self-adjoint Toeplitz operators, Summer Institute of Spectral Theory and Statistical Mechanics 1965, Brookhaven National Laboratory, Upton, New York, 1966. MR 34 #4084.
- 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
- Robert Ryan, The F. and M. Riesz theorem for vector measures, Nederl. Akad. Wetensch. Proc. Ser. A 66 = Indag. Math. 25 (1963), 408–412. MR 0152876
- Donald Sarason, Generalized interpolation in $H^{\infty }$, Trans. Amer. Math. Soc. 127 (1967), 179–203. MR 208383, DOI 10.1090/S0002-9947-1967-0208383-8 B. Sz-Nagy and C. Foiaş, Analyse harmonique des opérateurs de l’espace de Hilbert, Masson, Paris and Akad. Kiadó, Budapest, 1967. MR 37 #778. —, Dilatation des commutants d’opérateurs, C. R. Acad. Sci. Paris Sér. A-B 266 (1968), A493-A495. MR 38 #5049.
Additional Information
- © Copyright 1970 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 150 (1970), 529-539
- MSC: Primary 47.40
- DOI: https://doi.org/10.1090/S0002-9947-1970-0273449-3
- MathSciNet review: 0273449