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Raúl E. Curto and Woo Young Lee
Reduced Cowen Sets
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| Published: |
October 17, 2001
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| Keywords: |
Toeplitz operators, Hankel operators, hyponormal operators, reduced Cowen sets, Hermite-Fejér interpolation problem |
| Subject: |
Primary 47B35; Secondary 47B20, 30D50 |
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Abstract
For f∈ H2, let
G'f:={g∈ z H2: f+\bar g ∈ L∞ and
Tf+\bar g is hyponormal}.
In 1988, C. Cowen posed the following question:
If g∈ G'f is such that λg∉G'f (all λ∈C,
|λ|>1), is
g an extreme point of G'f?
In this note we answer this question in the negative. At the same time, we obtain
a general sufficient condition for the answer to be affirmative; that is, when
f∈ H∞ is such that rankH\bar f<∞.
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| Acknowledgements
The work of the first author was partially supported by NSF research grant DMS-9800931.
The work of the second author was partially supported by grant No. 2000-1-10100-002-3 from the Basic Research Program of the KOSEF
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| Author information
Raúl E. Curto:
Department of Mathematics, University of Iowa, Iowa City, IA 52242
curto@math.uiowa.edu
http://www.math.uiowa.edu/~curto/
Woo Young Lee:
Department of Mathematics, Sungkyunkwan University, Suwon 440-746, Korea
wylee@yurim.skku.ac.kr
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