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Extension with larger norm and separation with double support in normed linear spaces

Published online by Cambridge University Press:  17 April 2009

Ivan Singer
Ivan Singer
Affiliation:
Institutul Naţional pentru Creaţie Ştiinţificâ şi Tehnicâ, Bucureşti, Romania; Institutul de Matematicâ, Bucureşti, Romania.
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Abstract

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We prove, in normed linear spaces, the existence of extensions of continuous linear functionals from linear subspaces to the whole space, with arbitrarily prescribed larger norm. Also, we prove that under an additional boundedness assumption, in the known separation theorems for convex sets, there exist hyperplanes which separate and support both sets.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 21 , Issue 1 , February 1980 , pp. 93 - 105
Copyright
Copyright © Australian Mathematical Society 1980

References

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