 

Raúl E. Curto and Woo Young Lee
Reduced Cowen Sets


Published: 
October 17, 2001

Keywords: 
Toeplitz operators, Hankel operators, hyponormal operators, reduced Cowen sets, HermiteFejér interpolation problem 
Subject: 
Primary 47B35; Secondary 47B20, 30D50 


Abstract
For f∈ H^{2}, let
G'_{f}:={g∈ z H^{2}: f+\bar g ∈ L^{∞} and
T_{f+\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}<∞.


Acknowledgements
The work of the first author was partially supported by NSF research grant DMS9800931.
The work of the second author was partially supported by grant No. 20001101000023 from the Basic Research Program of the KOSEF


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 440746, Korea
wylee@yurim.skku.ac.kr

