Remote Access Journal of the American Mathematical Society
Green Open Access

Journal of the American Mathematical Society

ISSN 1088-6834(online) ISSN 0894-0347(print)



Common range of co-analytic Toeplitz operators

Author: John E. McCarthy
Journal: J. Amer. Math. Soc. 3 (1990), 793-799
MSC: Primary 47B35; Secondary 30D50
MathSciNet review: 1065054
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We characterise the intersection of the ranges of all co-analytic Toeplitz operators, by considering this set as the dual space of the Smirnov class in a certain topology.

References [Enhancements On Off] (What's this?)

  • John B. Conway, Subnormal operators, Research Notes in Mathematics, vol. 51, Pitman (Advanced Publishing Program), Boston, Mass.-London, 1981. MR 634507
  • Peter L. Duren, Theory of $H^{p}$ spaces, Pure and Applied Mathematics, Vol. 38, Academic Press, New York-London, 1970. MR 0268655
  • John B. Garnett, Bounded analytic functions, Pure and Applied Mathematics, vol. 96, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1981. MR 628971
  • Henry Helson, Large analytic functions. II, Analysis and partial differential equations, Lecture Notes in Pure and Appl. Math., vol. 122, Dekker, New York, 1990, pp. 217–220. MR 1044789
  • G. Köthe, Topological vector spaces I, Springer-Verlag, Heidelberg, 1969; Topological vector spaces II, Springer-Verlag, Heidelberg, 1979. J. E. M$^{c}$Carthy, Topologies on the Smirnov class (to appear). ---, Weighted Bergman spaces, Proceedings of a Conference on Function Spaces (Edwardsville, 1990) (to appear).
  • M. Nawrocki, Linear functionals on the Smirnov class of the unit ball in ${\bf C}^n$, Ann. Acad. Sci. Fenn. Ser. A I Math. 14 (1989), no. 2, 369–379. MR 1024438, DOI
  • F. Nevanlinna and R. Nevanlinna, Eigenschaften analytischer Funktionen in der Umgebung einer singulären Stelle oder Linie, Acta Soc. Sci. Fenn. (5) 50 (1922).
  • N. K. Nikol′skiĭ, Treatise on the shift operator, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 273, Springer-Verlag, Berlin, 1986. Spectral function theory; With an appendix by S. V. Hruščev [S. V. Khrushchëv] and V. V. Peller; Translated from the Russian by Jaak Peetre. MR 827223
  • Albert Wilansky, Modern methods in topological vector spaces, McGraw-Hill International Book Co., New York, 1978. MR 518316
  • Niro Yanagihara, Multipliers and linear functionals for the class $N^{+}$, Trans. Amer. Math. Soc. 180 (1973), 449–461. MR 338382, DOI

Similar Articles

Retrieve articles in Journal of the American Mathematical Society with MSC: 47B35, 30D50

Retrieve articles in all journals with MSC: 47B35, 30D50

Additional Information

Article copyright: © Copyright 1990 American Mathematical Society