Polynomially bounded operators and Ext groups

Author:
Sarah H. Ferguson

Journal:
Proc. Amer. Math. Soc. **124** (1996), 2779-2785

MSC (1991):
Primary 47B38; Secondary 18G15

MathSciNet review:
1327011

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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper, we consider the Ext functor in the category

of Hilbert modules over the disk algebra. We characterize the group

as a quotient of operators and explicitly calculate

, where is a weighted Hardy space. We then use our results to give a simple proof of a result due to Bourgain.

**1.**J. Bourgain,*On the similarity problem for polynomially bounded operators on Hilbert space*, Israel J. Math.**54**(1986), no. 2, 227–241. MR**852479**, 10.1007/BF02764943**2.**J. F. Carlson and D. N. Clark,*Cohomology and extensions of Hilbert modules*, J.Functional Analysis 128 (1995).**3.**J. F. Carlson, D. N. Clark, C. Foias and J. P. Williams,*Projective Hilbert A(D)-Modules*, New York J. Math. 1 (1994), 26--38. CMP**94:15****4.**Ronald G. Douglas and Vern I. Paulsen,*Hilbert modules over function algebras*, Pitman Research Notes in Mathematics Series, vol. 217, Longman Scientific & Technical, Harlow; copublished in the United States with John Wiley & Sons, Inc., New York, 1989. MR**1028546****5.**C. Foias and J. P. Williams,*On a class of polynomially bounded operators*, preprint (1974).**6.**Vladimir V. Peller,*Estimates of functions of power bounded operators on Hilbert spaces*, J. Operator Theory**7**(1982), no. 2, 341–372. MR**658618****7.**Allen L. Shields,*Weighted shift operators and analytic function theory*, Topics in operator theory, Amer. Math. Soc., Providence, R.I., 1974, pp. 49–128. Math. Surveys, No. 13. MR**0361899****8.**Ke He Zhu,*Operator theory in function spaces*, Monographs and Textbooks in Pure and Applied Mathematics, vol. 139, Marcel Dekker, Inc., New York, 1990. MR**1074007**

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Additional Information

**Sarah H. Ferguson**

Email:
sarah@math.uh.edu

DOI:
https://doi.org/10.1090/S0002-9939-96-03340-0

Keywords:
Polynomially bounded operator,
Ext groups,
reproducing kernel Hilbert space,
weighted Hardy space,
BMOA

Received by editor(s):
March 13, 1995

Communicated by:
Palle E. T. Jorgensen

Article copyright:
© Copyright 1996
American Mathematical Society