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Journal of Operator Theory

Volume 38, Issue 2, Fall 1997  pp. 329-365.

Flag manifolds and the Cowen-Douglas theory

Authors Mircea Martin (1) and Norberto Salinas (2)
Author institution: (1) Department of Mathematics, Baker University, Baldwin City, KS 66006, U.S.A.
(2) Department of Mathematics, University of Kansas, Lawrence, KS 66045, U.S.A.

Summary:  The present article focuses on the congruence problem for holomorphic maps into flag manifolds associated with C*-algebras and the equivalence problem for tuples of elements of a C*-algebra in the Cowen-Douglas class. The former problem is formulated and solved for a quite large class of holomorphic maps that includes the kind of maps needed to address and solve the latter problem. Along the way towards manageable answers to both these problems we also study in detail the behavior of holomorphic families of elements with closed range of C*-algebras.

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