TY - JOUR
T1 - Boundary values and Cowen-Douglas curvature
AU - McCarthy, John E.
N1 - Funding Information:
* The author was partially supported by National Science Foundation Grant DMS 9296099.
PY - 1996/4/10
Y1 - 1996/4/10
N2 - We define a metric in terms of the Cowen-Douglas curvature for an operator T in B1(Ω). Any boundary point of Ω that is a finite distance, with respect to this metric, from the eigenvalues in the interior is itself an eigenvalue of T. If T is represented as the adjoint of multiplication by the coordinate function on some holomorphic Hilbert space on Ω, this gives a condition under which functions in the space have limits along a path going to the boundary of Ω.
AB - We define a metric in terms of the Cowen-Douglas curvature for an operator T in B1(Ω). Any boundary point of Ω that is a finite distance, with respect to this metric, from the eigenvalues in the interior is itself an eigenvalue of T. If T is represented as the adjoint of multiplication by the coordinate function on some holomorphic Hilbert space on Ω, this gives a condition under which functions in the space have limits along a path going to the boundary of Ω.
UR - https://www.scopus.com/pages/publications/0030577884
U2 - 10.1006/jfan.1996.0038
DO - 10.1006/jfan.1996.0038
M3 - Article
AN - SCOPUS:0030577884
SN - 0022-1236
VL - 137
SP - 1
EP - 18
JO - Journal of Functional Analysis
JF - Journal of Functional Analysis
IS - 1
ER -