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On power bounded operators
Author(s):
Eugen
J.
Ionascu
Journal:
Proc. Amer. Math. Soc.
125
(1997),
1435-1441.
MSC (1991):
Primary 47B99
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.
References:
- 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:
10.1090/S0002-9939-97-03623-X
PII:
S 0002-9939(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
Copyright of article:
Copyright
1997,
American Mathematical Society
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