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# Univalently Induced, Closed Range, Composition Operators on the Bloch-type Spaces

Published:2011-04-06
Printed: Jun 2012
• 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
 MSC Classifications: 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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