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 power bounded operators

Author: Eugen J. Ionascu
Journal: Proc. Amer. Math. Soc. 125 (1997), 1435-1441
MSC (1991): Primary 47B99
MathSciNet review: 1353387
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we generalize the following consequence of a well-known result of Nagy: if $T$ and $T^{-1}$ are power bounded operators, then $T$ is a polynomially bounded operator.

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

  • 1. A. Lebow, A power-bounded operator that is not polynomially bounded, Michigan Math. J. 15 (1968), 397-399. MR 38:5047
  • 2. S. R. Foguel, A counterexample to a problem of Sz.-Nagy, Proc. Amer. Math. Soc. 13 (1964), 788-790. MR 29:2646
  • 3. B. Sz.-Nagy, On uniformly bounded linear transformations in Hilbert space, Acta Sci. Math. (Szeged) 11 (1947), 152-157. MR 9:191
  • 4. P. R. Halmos, On Foguel's answer to Nagy's question, Proc. Amer. Math. Soc. 13 (1964), 791-793. MR 29:2647
  • 5. P. R. Halmos, Ten problems in Hilbert space, Bull. Amer. Math. Soc. 76 (1970), 887-933. MR 42:5066

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 47B99

Retrieve articles in all journals with MSC (1991): 47B99

Additional Information

Eugen J. Ionascu
Affiliation: Department of Mathematics, Texas A& M University, College Station, Texas 77843

Received by editor(s): June 19, 1995
Received by editor(s) in revised form: November 20, 1995
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1997 American Mathematical Society

American Mathematical Society