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)

 
 

 

Bimodules over nest algebras
and Deddens' theorem


Author: I. Todorov
Journal: Proc. Amer. Math. Soc. 127 (1999), 1771-1780
MSC (1991): Primary 47D15; Secondary 47D25
DOI: https://doi.org/10.1090/S0002-9939-99-05115-1
Published electronically: February 11, 1999
MathSciNet review: 1637440
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We generalize Deddens' theorem for nest algebras in the case of w*-closed nest algebras bimodules. For each such bimodule, we introduce a norm closed sub-bimodule of it, which corresponds to the radical of a nest algebra and describe it in a number of ways, generalizing known facts about nest algebras.


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

  • 1. K. R. Davidson, Nest algebras. Triangular forms for operator algebras on Hilbert spaces, Longman, 1988. MR 90f:47062
  • 2. J. A. Deddens, Another description of nest algebras, Hilbert space operators, Lecture Notes in Math. 693, Springer, New York, (1978), 77-86. MR 80f:47033
  • 3. J. A. Erdos, On some ideals of nest algebras, Proc. London Math. Soc. (3) 44 (1982), 143-160. MR 83g:47045
  • 4. J. A. Erdos Operators of finite rank in nest algebras, J. London Math. Soc. 43 (1968), 391-397. MR 37:5721
  • 5. J. A. Erdos, Reflexivity for subspace maps and linear spaces of operators, Proc. London Math. Soc. (3) 52 (1986), 582-600. MR 87h:47103
  • 6. J. A. Erdos and W. E. Longstaff, The convergence of triangular integrals of operators on Hilbert space, Indiana Univ. Math. J. 22 (1973), 929-938. MR 49:1178
  • 7. J. A. Erdos and S. C. Power, Weakly closed ideals of nest algebras, J. Operator Theory 7 (1982), 219-235. MR 84a:47056
  • 8. S. Karanasios, Triangular integration with respect to a nest algebra module, Indiana Univ. Math. J. 34 (1985), 299-317. MR 86h:47073
  • 9. R. I. Loebl and P. S. Muhly, Analycity and flows in von Neumann algebras, J. Funct. Anal. 29 (1978), 214-252. MR 81h:46080
  • 10. D. I. Marculescu, Reflexivity of linear manifolds of operators, Doctoral thesis, University of London, 1984.
  • 11. M. Radjabalipour, Operators commuting with positive operators, Proc. Amer. Math. Soc. 77 (1979), 107-110. MR 81d:47014
  • 12. J. R. Ringrose, On some algebras of operators, Proc. London Math. Soc. (3) 15 (1965), 61-83. MR 30:1405
  • 13. A. I. Loginov and V. S. Shulman, Hereditary and intermediate reflexivity of $W^*$-algebras, (Russian) Izv. Akad. Nauk. SSSR Ser. Mat. 39 (1975), 1260-1273; English translation, Math. USSR-Izv. 9 (1975), 1189-1201. MR 53:8919

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 47D15, 47D25

Retrieve articles in all journals with MSC (1991): 47D15, 47D25


Additional Information

I. Todorov
Affiliation: Department of Mathematics, University of Athens, Panepistemioupolis 15784, Athens, Greece
Email: itodorov@atlas.uoa.gr

DOI: https://doi.org/10.1090/S0002-9939-99-05115-1
Keywords: Bimodule, nest algebra, spectral nest, Deddens' theorem
Received by editor(s): September 16, 1997
Published electronically: February 11, 1999
Additional Notes: This work was supported by a grant of the Greek State Scholarship Foundation
Communicated by: David R. Larson
Article copyright: © Copyright 1999 American Mathematical Society

American Mathematical Society