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COMPACT DIFFERENCES OF COMPOSITION OPERATORS

Part of: Special classes of linear operators

Published online by Cambridge University Press:  01 February 2008

ELKE WOLF
ELKE WOLF*
Affiliation:
Mathematical Institute, University of Paderborn, D-33095 Paderborn, Germany (email: lichte@math.uni-paderborn.de)
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Abstract

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Let ϕ and ψ be analytic self-maps of the open unit disk. Each of them induces a composition operator, Cϕ and Cψ respectively, acting between weighted Bergman spaces of infinite order. We show that the difference Cϕ−Cψ is compact if and only if both operators are compact or both operators are not compact and the pseudohyperbolic distance of the functions ϕ and ψ tends to zero if ∣ϕ(z)∣→1 or ∣ψ(z)∣→1.

Keywords

differences of weighted composition operatorscompactweighted Bergman spaces of infinite order

MSC classification

Secondary: 47B33: Composition operators 47B38: Operators on function spaces (general)
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 77 , Issue 1 , February 2008 , pp. 161 - 165
Copyright
Copyright © Australian Mathematical Society 2008

References

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