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

DOI:
https://doi.org/10.1090/S0002-9939-1978-0493397-6

MathSciNet review:
0493397

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Let be an arbitrary subalgebra of and let be a dense operator range invariant under such that every nonzero operator range invariant under contains . Then the closure of in the strong operator topology is .

**[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)**

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

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

Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1978-0493397-6

Keywords:
Invariant subspace,
transitive operator algebra,
operator ranges

Article copyright:
© Copyright 1978
American Mathematical Society