Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Subnormal composition operators


Author: Alan Lambert
Journal: Proc. Amer. Math. Soc. 103 (1988), 750-754
MSC: Primary 47B20; Secondary 47B38
DOI: https://doi.org/10.1090/S0002-9939-1988-0947651-8
MathSciNet review: 947651
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ C$ be the composition operator on $ {L^2}(X,\Sigma ,m)$ given by $ Cf = f \circ T$, where $ T$ is a $ \Sigma $-measurable transformation from $ X$ onto $ X$ and $ {T^{ - 1}}/dm$ is strictly positive and bounded. It is shown that $ C$ is a subnormal operator if and only if the sequence $ dm \circ {T^{ - n}}/dm$ is a moment sequence for almost every point in $ X$. Several examples of subnormal composition operators are included.


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

  • [1] P. Dibrell and J. Campbell, Hyponormal powers of composition operators, Proc. Amer. Math. Soc. 102 (1988), 914-918. MR 934867 (89f:47045)
  • [2] D. Harrington and R. Whitley, Seminormal composition operators, J. Operator Theory 11 (1984), 125-135. MR 739797 (85j:47034)
  • [3] A. Lambert, Subnormality and weighted shifts, J. London Math. Soc. (2) 14 (1976), 476-480. MR 0435915 (55:8866)
  • [4] -, Hyponormal composition operators, Bull. London Math. Soc. 18 (1986), 395-400. MR 838810 (87h:47059)
  • [5] E. Nordgren, Composition operators in Hilbert space, Hilbert Space Operators, Lecture Notes in Math., vol. 639, Springer-Verlag, Berlin and New York, 1978. MR 526531 (80d:47046)
  • [6] A Shields, Weighted shift operators and analytic function theory, Topics in Operator Theory, Math. Surveys, no. 13, Amer. Math. Soc., Providence, R. I., 1974. MR 0361899 (50:14341)
  • [7] R. Singh and A. Kumar, Characterization of invertible, unitary, and normal composition operators, Bull. Austral. Math. Soc. 19 (1978), 81-95. MR 522183 (80e:47030)
  • [8] R. Singh, A. Kumar, and D. Gupta, Quasinormal composition operators on $ l_p^2$, Indian J. Pure Appl. Math. 11 (7) (1980), 904-907. MR 577352 (81g:47030)
  • [9] R. Whitley, Normal and quasinormal composition operators, Proc. Amer. Math. Soc. 76 (1978), 114-118. MR 492057 (81a:47033)
  • [10] D. Widder, The Laplace transform, Princeton Univ. Press, Princeton, N. J., 1946.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 47B20, 47B38

Retrieve articles in all journals with MSC: 47B20, 47B38


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1988-0947651-8
Article copyright: © Copyright 1988 American Mathematical Society

American Mathematical Society