Tohoku Mathematical Journal
2008
September
SECOND SERIES VOL. 60, NO. 3

Tohoku Math. J.
60 (2008), 423-440

Title INTERPOLATION AND COMPLEX SYMMETRY

Author Stephan R. Garcia and Mihai Putinar

(Received August 22, 2007)
Abstract. In a separable complex Hilbert space endowed with an isometric conjugate-linear involution, we study sequences orthonormal with respect to an associated bilinear form. Properties of such sequences are measured by a positive, possibly unbounded angle operator which is formally orthogonal as a matrix. Although developed in an abstract setting, this framework is relevant to a variety of eigenvector interpolation problems arising in function theory and in the study of differential operators.

2000 Mathematics Subject Classification. Primary 30D55; Secondary 47A15.
Key words and phrases. Complex symmetric operator, interpolation, eigensystem, eigenfunction, contraction, conjugation, dissipative operator, bilinear form, inner function, compressed Toeplitz operator.

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