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Iterated Aluthge transforms of composition operators on H-2

Title
Iterated Aluthge transforms of composition operators on H-2
Authors
Jung, SungeunKim, YoenhaKo, Eungil
Ewha Authors
고응일김연하
SCOPUS Author ID
고응일scopus
Issue Date
2015
Journal Title
INTERNATIONAL JOURNAL OF MATHEMATICS
ISSN
0129-167XJCR Link1793-6519JCR Link
Citation
vol. 26, no. 10
Keywords
Composition operatorweighted composition operatorAluthge transformiterated Aluthge transform
Publisher
WORLD SCIENTIFIC PUBL CO PTE LTD
Indexed
SCI; SCIE; SCOPUS WOS scopus
Abstract
In this paper, we study various properties of the iterated Aluthge transforms of the composition operators C-phi and C-sigma where phi(z) = az + (1 - a) and sigma(z) = az/-(1-a)z+1 for 0 < a < 1. We express the iterated Aluthge transforms (C) over tilde ((n))(phi) wand (C) over tilde ((n))(sigma) as weighted composition operators with linear fractional symbols. As a corollary, we prove that ( n). (C) over tilde ((n))(phi) and (C) over tilde ((n))(sigma) are not quasinormal but binormal. In addition, we show that (C) over tilde ((n))(phi) and (C) over tilde ((n))(sigma) are quasisimilar for all non-negative integers n and m. Finally, we show that {(C) over tilde ((n))(phi)} and {(C) over tilde ((n))(sigma)} converge to normal operators in the strong operator topology.
DOI
10.1142/S0129167X15500792
Appears in Collections:
자연과학대학 > 수학전공 > Journal papers
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