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 , 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 , and applies even to linear spaces of operators. Our result contains the reflexivity theorems of [**3**,**2** and **9**] as particular cases.

**[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, -*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*, 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*-*algebras*, Izv. Akad. Nauk SSSR Ser. Mat.**39**(1975), 1260-1273. (Russian) MR**0405124 (53:8919)****[9]**G. Robel,*On the structure of*-*operators and related algebras*. I, J. Operator Theory**12**(1984), 23-45. MR**757111 (86f:47011a)**

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