# A note on the existence, uniqueness and symmetry of par-balanced realizations

Article

- Received:
- Revised:

DOI: 10.1007/BF01192830

- Cite this article as:
- Gheondea, A. & Ober, R.J. Integr equ oper theory (2000) 37: 423. doi:10.1007/BF01192830

- 2 Citations
- 30 Downloads

## Abstract

We give a proof of the realization theorem of N.J. Young which states that analytic functions which are symbols of bounded Hankel operators admit par-balanced realizations. The main tool used in this proof is the induced Hilbert spaces and a lifting lemma of Kreîn-Reid-Lax-Dieudonné. Alternatively one can use the Loewner inequality. A short proof of the uniqueness of par-balanced realizations is included. As an application, it is proved that par-balanced realizations of real symmetric transfer functions are*J*-self-adjoint.

### Mathematics Subject Classification

93B1593B2847B3547B50## Copyright information

© Birkhäuser Verlag 2000