IAM   02674
INSTITUTO ARGENTINO DE MATEMATICA ALBERTO CALDERON
Unidad Ejecutora - UE
artículos
Título:
Paths of inner-related functions
Autor/es:
A. NICOLAU Y D. SUAREZ
Revista:
JOURNAL OF FUNCTIONAL ANALYSIS
Editorial:
ACADEMIC PRESS INC ELSEVIER SCIENCE
Referencias:
Año: 2012 vol. 262 p. 3749 - 3749
ISSN:
0022-1236
Resumen:
We characterize the connected components of the subset CN∗ of H∞ formed by the products bh, where b is Carleson–Newman Blaschke product and h ∈ H∞ is an invertible function. We use this result to show that, except for finite Blaschke products, no inner function in the little Bloch space is in the closure of one of these components. Our main result says that every inner function can be connected with an element of CN∗ within the set of products uh, where u is inner and h is invertible. We also study some of these issues in the context of Douglas algebras.