A polynomially bounded operator

on Hilbert space

which is not similar to a contraction

Author:
Gilles Pisier

Journal:
J. Amer. Math. Soc. **10** (1997), 351-369

MSC (1991):
Primary 47A20, 47B35, 47D25, 47B47; Secondary 47A56, 42B30

DOI:
https://doi.org/10.1090/S0894-0347-97-00227-0

MathSciNet review:
1415321

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Let . We prove that there exists an operator such that for any polynomial we have , but is not similar to a contraction, *i.e.* there does not exist an invertible operator such that . This answers negatively a question attributed to Halmos after his well-known 1970 paper (``Ten problems in Hilbert space"). We also give some related finite-dimensional estimates.

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Additional Information

**Gilles Pisier**

Affiliation:
Department of Mathematics, Texas A&M University, College Station, Texas 77843;
Université Paris VI, Equipe d’Analyse, Case 186, 75252 Paris Cedex 05, France

Email:
gip@ccr.jussieu.fr

DOI:
https://doi.org/10.1090/S0894-0347-97-00227-0

Received by editor(s):
March 11, 1996

Received by editor(s) in revised form:
October 11, 1996

Article copyright:
© Copyright 1997
American Mathematical Society