Infinite dimensional universal subspaces generated by Blaschke products

Author:
Raymond Mortini

Journal:
Proc. Amer. Math. Soc. **135** (2007), 1795-1801

MSC (2000):
Primary 30D50; Secondary 47B33, 46J15, 30H05

Published electronically:
December 28, 2006

MathSciNet review:
2286090

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be the Banach algebra of all bounded analytic functions in the unit disk . A function is said to be universal with respect to the sequence of noneuclidian translates, if the set is locally uniformly dense in the set of all holomorphic functions bounded by . We show that for any sequence of points in tending to the boundary there exists a closed subspace of , topologically generated by Blaschke products, and linear isometric to , such that all of its elements are universal with respect to noneuclidian translates. The proof is based on certain interpolation problems in the corona of . Results on cyclicity of composition operators in are deduced.

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Additional Information

**Raymond Mortini**

Affiliation:
Département de Mathématiques, Université Paul Verlaine, Ile du Saulcy F-57045 Metz, France

Email:
mortini@math.univ-metz.fr

DOI:
http://dx.doi.org/10.1090/S0002-9939-06-08669-2

Keywords:
Universal Blaschke products,
interpolation in the corona,
composition operators on Hardy spaces,
joint cyclic vectors

Received by editor(s):
September 6, 2005

Received by editor(s) in revised form:
February 5, 2006

Published electronically:
December 28, 2006

Additional Notes:
The author thanks the referee for his/her comments improving the exposition of this work

Communicated by:
Joseph A. Ball

Article copyright:
© Copyright 2006
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.