# 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.

**Keywords:**De Branges spaces, multiplication by a finite Blaschke product, invariant subspaces.

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