Previous issue ·  Next issue ·  Most recent issue · All issues

# Journal of Operator Theory

Volume 37, Issue 2, Spring 1997  pp. 223-245.

Multiplication by finite Blaschke factors on de Branges spaces

Authors Dinesh Singh (1) and Virender Thukral (2)
Author institution: (1) Department of Mathematics, University of Delhi, Delhi 110007, INDIA. Current address: Indian Statistical Institute, 7 S.J.S. Sansanwal Marg, New Delhi 110016, INDIA
(2) Department of Mathematics, University of Delhi, Delhi 110007, INDIA

Summary:  This note characterizes those Hilbert spaces which are algebraically contained in the Hardy space H^2 of scalar valued analytic functions on the open unit disk $\mathbb D$ and on which multiplication by a finite Blaschke product acts as an isometry. A general inner-outer factorization is deduced and some other properties of the operator of multiplication by a finite Blaschke product are described. The main theorem generalizes a recent theorem of de Branges as well as a theorem of Peter Lax.

Contents    Full-Text PDF