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Composition operators on Banach function spaces

Authors: Rajeev Kumar and Romesh Kumar
Journal: Proc. Amer. Math. Soc. 133 (2005), 2109-2118
MSC (2000): Primary 47B33, 46E30; Secondary 47B07, 46B70
Published electronically: February 15, 2005
MathSciNet review: 2137878
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Abstract: We study the boundedness and the compactness of composition operators on some Banach function spaces such as absolutely continuous Banach function spaces on a $\sigma$-finite measure space, Lorentz function spaces on a $\sigma$-finite measure space and rearrangement invariant spaces on a resonant measure space. In addition, we study some properties of the spectra of a composition operator on the general Banach function spaces.

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Additional Information

Rajeev Kumar
Affiliation: Department of Mathematics, University of Jammu, Jammu-180 006, India

Romesh Kumar
Affiliation: Department of Mathematics, University of Jammu, Jammu-180 006, India

Keywords: Banach function spaces, compact operators, composition operators, Lorentz spaces, measurable transformation, rearrangement invariant spaces
Received by editor(s): January 24, 2004
Received by editor(s) in revised form: April 5, 2004
Published electronically: February 15, 2005
Additional Notes: The first author was supported in part by CSIR Grant #9(96)100/2002-EMR-I, dated–13-5-2002).
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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