On power bounded operators

Author:
Eugen J. Ionascu

Journal:
Proc. Amer. Math. Soc. **125** (1997), 1435-1441

MSC (1991):
Primary 47B99

DOI:
https://doi.org/10.1090/S0002-9939-97-03623-X

MathSciNet review:
1353387

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

**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**

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Additional Information

**Eugen J. Ionascu**

Affiliation:
Department of Mathematics, Texas A& M University, College Station, Texas 77843

DOI:
https://doi.org/10.1090/S0002-9939-97-03623-X

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