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The minimum modulus of Blaschke products

โœ Scribed by C.L Belna; G.T Cargo

Publisher
Elsevier Science
Year
1984
Tongue
English
Weight
373 KB
Volume
104
Category
Article
ISSN
0022-247X

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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

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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