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Polynomially bounded operators and Ext groups
Author(s):
Sarah
H.
Ferguson
Journal:
Proc. Amer. Math. Soc.
124
(1996),
2779-2785.
MSC (1991):
Primary 47B38;
Secondary 18G15
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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.
References:
- 1.
- J. Bourgain, The Similarity Problem for polynomially bounded operators on Hilbert space, Israel Journal of Math., Vol. 54, No. 2, (1986). MR 88h:47024
- 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.
- R. G. Douglas and V. I. Paulsen, Hilbert modules over function algebras, Longman Scientific & Technical, New York (1989). MR 91g:46084
- 5.
- C. Foias and J. P. Williams, On a class of polynomially bounded operators, preprint (1974).
- 6.
- V. V. Peller, Estimates of functions of power bounded operators on Hilbert spaces, J. Operator Theory, 7 (1982), 341--372. MR 83i:47019
- 7.
- A. Shields, Weighted shift operators and analytic function theory, Topics in Operator Theory, Math. Surveys, No. 13, Amer. Math. Soc., Providence, R.I. (1974) MR 50:14341
- 8.
- K. Zhu, Operator Theory in function spaces, Marcel Dekker, Inc., New York and Basel (1990). MR 92c:47031
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Additional Information:
Sarah
H.
Ferguson
Affiliation:
Department of Mathematics, University of Houston, Houston, Texas 77204-3476
Email:
sarah@math.uh.edu
DOI:
10.1090/S0002-9939-96-03340-0
PII:
S 0002-9939(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
Copyright of article:
Copyright
1996,
American Mathematical Society
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