#### Title

Tridiagonal Reproducing Kernels and Subnormality

#### Publication Date

2013

#### Journal

Journal of Operator Theory

#### Volume

70

#### Issue

2

#### First Page

477

#### Last Page

494

#### Department

Mathematics

#### Abstract

We consider analytic reproducing kernel Hilbert spaces H with orthonormal bases of the form {(a(n) + b(n)z)z(n) : n >= 0}. If b(n) = 0 for all n, then H is a diagonal space and multiplication by z, M-z, is a weighted shift. Our focus is on providing extensive classes of examples for which M-z is a bounded subnormal operator on a tridiagonal space H where b(n) not equal 0. The Aronszajn sum of H and (1 - z)H where H is either the Hardy space or the Bergman space on the disk are two such examples.

#### Link to Published Version

#### Recommended Citation

Adams, Gregory; Feldman, Nathan S.; and McGuire, Paul. "Tridiagonal Reproducing Kernels and Subnormality." *Journal of Operator Theory* (2013)
: 477-494.