Let A be a contraction on Hilbert space H and ฯ a finite Blaschke product. In this paper, we consider the problem when the norm of ฯ(A) is equal to 1. We show that (1) ฯ(A) = 1 if and only if A k = 1, where k is the number of zeros of ฯ counting multiplicity, and (2) if H is finite-dimensional and A
โฆ LIBER โฆ
Centralizers of finite Blaschke products
โ Scribed by Carlos Arteaga
- Publisher
- Springer
- Year
- 2000
- Tongue
- English
- Weight
- 448 KB
- Volume
- 31
- Category
- Article
- ISSN
- 1678-7714
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## Introduction Let S be the unit circle. We call a (measureable) bijection . : S ร S absolutely continuous if for any A/S, \*(A)=0 if and only if \*(.(A))=0, where \* denotes normalised Lebesgue (arc) measure on S. We consider (finite) nontrivial (i.e. not 1:1 or constant) Blaschke products whic