Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

A reflexivity theorem for weakly closed subspaces of operators


Author: Hari Bercovici
Journal: Trans. Amer. Math. Soc. 288 (1985), 139-146
MSC: Primary 47D15; Secondary 47A15
DOI: https://doi.org/10.1090/S0002-9947-1985-0773052-3
MathSciNet review: 773052
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: It was proved in [4] that the ultraweakly closed algebras generated by certain contractions on Hilbert space have a remarkable property. This property, in conjunction with the fact that these algebras are isomorphic to $ {H^\infty }$, was used in [3] to show that such ultraweakly closed algebras are reflexive. In the present paper we prove an analogous result that does not require isomorphism with $ {H^\infty }$, and applies even to linear spaces of operators. Our result contains the reflexivity theorems of [3,2 and 9] as particular cases.


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

  • [1] C. Apostol, H. Bercovoci, C. Foias and C. Pearcy, Invariant subspaces, dilation theory, and the structure of the predual of a dual operator algebra. I, J. Functional Anal. (to appear).
  • [2] H. Bercovici, B. Chevreau, C. Foias and C. Pearcy, Dilation theory and systems of simultaneous equations in the predual of an operator algebra. II, Math. Z. 187 (1984), 97-103. MR 753424 (85k:47090)
  • [3] H. Bercovici, C. Foias, J. Langsam and C. Pearcy, $ (BCP)$-operators are reflexive, Michigan Math. J. 29 (1982), 371-379. MR 674290 (84a:47007)
  • [4] H. Bercovici, C. Foias and C. Pearcy, Factoring trace-class operator-valued functions with applications to the class $ {{\mathbf{A}}_{{\aleph _0}}}$, J. Operator Theory (to appear). MR 808297 (87a:47014)
  • [5] -, Dilation theory and systems of simultaneous equations in the predual of an operator algebra. I, Michigan Math. J. 30 (1983), 335-354. MR 725785 (85k:47089)
  • [6] A. Brown and C. Pearcy, Introduction to operator theory. I. Elements of functional analysis, Springer, New York, 1977. MR 0511596 (58:23463)
  • [7] D. W. Hadwin and E. A. Nordgren, Subalgebras of reflexive algebras, J. Operator Theory 7 (1982), 3-23. MR 650190 (83f:47033)
  • [8] A. I. Loginov and V. S. Sulman, Hereditary and intermediate reflexivity of $ {W^\ast}$-algebras, Izv. Akad. Nauk SSSR Ser. Mat. 39 (1975), 1260-1273. (Russian) MR 0405124 (53:8919)
  • [9] G. Robel, On the structure of $ (BCP)$-operators and related algebras. I, J. Operator Theory 12 (1984), 23-45. MR 757111 (86f:47011a)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 47D15, 47A15

Retrieve articles in all journals with MSC: 47D15, 47A15


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1985-0773052-3
Article copyright: © Copyright 1985 American Mathematical Society

American Mathematical Society