New York Journal of Mathematics
Volume 7 (2001) 217-222


Raúl E. Curto and Woo Young Lee

Reduced Cowen Sets

Published: October 17, 2001
Keywords: Toeplitz operators, Hankel operators, hyponormal operators, reduced Cowen sets, Hermite-Fejér interpolation problem
Subject: Primary 47B35; Secondary 47B20, 30D50

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<∞.


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

Author information

Raúl E. Curto:
Department of Mathematics, University of Iowa, Iowa City, IA 52242

Woo Young Lee:
Department of Mathematics, Sungkyunkwan University, Suwon 440-746, Korea