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On strong convex compactness property of spaces of nonlinear operators

Published online by Cambridge University Press:  17 April 2009

Xueli Song  and
Jigen Peng
Xueli Song
Affiliation:
Department of Mathematics, Xi'an Jiaotong University, Xi'an 710049, China, e-mail: songx1810@sohu.com, jgpeng@mail.xjtu.edu.cn
Jigen Peng
Affiliation:
Department of Mathematics, Xi'an Jiaotong University, Xi'an 710049, China, e-mail: songx1810@sohu.com, jgpeng@mail.xjtu.edu.cn
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The strong convex compactness property is important for property persistence of operator semigroups under perturbations. It has been investigated in the linear setting. In this paper, we are concerned with the property in the nonlinear setting. We prove that the following spaces of (nonlinear) operators enjoy the strong convex compactness property: the space of compact operators, the space of completely continuous operators, the space of weakly compact operators, the space of conditionally weakly compact operators, the space of weakly completely continuous operators, the space of demicontinuous operators, the space of weakly continuous operators and the space of strongly continuous operators. Moreover, we prove the property persistence of operator semigroups under nonlinear perturbation.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 74 , Issue 3 , December 2006 , pp. 411 - 418
Copyright
Copyright © Australian Mathematical Society 2006

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