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MEASURES OF NONCOMPACTNESS IN ULTRAPRODUCTS

Published online by Cambridge University Press:  08 June 2009

WIESŁAWA KACZOR*
Affiliation:
Instytut Matematyki UMCS, 20-031 Lublin, Poland (email: [email protected])
ADAM STACHURA
Affiliation:
Institute of Mathematics and Computer Science, John Paul II Catholic University of Lublin, 20-708 Lublin, Poland (email: [email protected])
JUSTYNA WALCZUK
Affiliation:
Instytut Matematyki PWSZ, 22-400 Zamość, Poland (email: [email protected])
MAGDALENA ZOŁA
Affiliation:
Institute of Mathematics and Computer Science, John Paul II Catholic University of Lublin, 20-708 Lublin, Poland (email: [email protected])
*
For correspondence; e-mail: [email protected]
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Abstract

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We investigate the connection between measures of noncompactness of a bounded subset of a given Banach space and the corresponding measures of noncompactness of an ultrapower of this subset. The Kuratowski, Hausdorff and separation measures of noncompactness are considered. We prove that in the first two cases the measures of a subset are equal to the respective measures of ultrapowers of this subset. In the case of separation measure of noncompactness, the equality is not necessarily fulfilled.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 2009

References

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