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)



On density of algebras with minimal invariant operator ranges

Author: Heydar Radjavi
Journal: Proc. Amer. Math. Soc. 68 (1978), 189-192
MSC: Primary 46L15; Secondary 47A15
MathSciNet review: 0493397
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ \mathfrak{A}$ be an arbitrary subalgebra of $ \mathcal{B}(\mathcal{H})$ and let $ \mathfrak{M}$ be a dense operator range invariant under $ \mathfrak{A}$ such that every nonzero operator range invariant under $ \mathfrak{A}$ contains $ \mathfrak{M}$. Then the closure of $ \mathfrak{A}$ in the strong operator topology is $ \mathcal{B}(\mathcal{H})$.

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

  • [1] Edward A. Azoff, Invariant linear manifold and the self-adjointness of operator algebras, Amer. J. Math. 99 (1977), 121-137. MR 0435886 (55:8837)
  • [2] R. G. Douglas, On majorization, factorization, and range inclusion of operators on Hilbert space, Proc. Amer. Math. Soc. 17 (1966), 413-415. MR 0203464 (34:3315)
  • [3] R. G. Douglas and C. Foiaş, Infinite dimensional versions of a theorem of Brickman-Fillmore, Indiana Univ. Math. J. 25 (1976), 315-320. MR 0407622 (53:11394)
  • [4] P. A. Fillmore and J. P. Williams, On operator ranges, Advances in Math. 7 (1971), 254-281. MR 0293441 (45:2518)
  • [5] C. Foiaş, Invariant para-closed subspaces, Indiana Univ. Math. J. 21 (1972), 887-906. MR 0293439 (45:2516)
  • [6] E. Nordgren, H. Radjavi and P. Rosenthal, Operator algebras leaving compact operator ranges invariant, Michigan Math. J. 23 (1976), 375-377. MR 0458200 (56:16403)
  • [7] H. Radjavi and P. Rosenthal, Invariant subspaces, Springer-Verlag, Berlin and New York, 1973. MR 0367682 (51:3924)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 46L15, 47A15

Retrieve articles in all journals with MSC: 46L15, 47A15

Additional Information

Keywords: Invariant subspace, transitive operator algebra, operator ranges
Article copyright: © Copyright 1978 American Mathematical Society

American Mathematical Society