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Univalently Induced, Closed Range, Composition Operators on the Bloch-type Spaces
  Published:2011-04-06
 Printed: Jun 2012
Canadian Mathematical Bulletin
  • Nina Zorboska,
    Department of Mathematics, University of Manitoba, Winnipeg, MB, R3T 2N2
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Abstract

While there is a large variety of univalently induced closed range composition operators on the Bloch space, we show that the only univalently induced, closed range, composition operators on the Bloch-type spaces $B^{\alpha}$ with $\alpha \ne 1$ are the ones induced by a disc automorphism.
Keywords: composition operators, Bloch-type spaces, closed range, univalent composition operators, Bloch-type spaces, closed range, univalent
MSC Classifications: 47B35, 32A18 show english descriptions Toeplitz operators, Hankel operators, Wiener-Hopf operators [See also 45P05, 47G10 for other integral operators; see also 32A25, 32M15]
Bloch functions, normal functions 47B35 - Toeplitz operators, Hankel operators, Wiener-Hopf operators [See also 45P05, 47G10 for other integral operators; see also 32A25, 32M15]
32A18 - Bloch functions, normal functions
 
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