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Banach Envelopes of Non-Locally Convex Spaces

Published online by Cambridge University Press:  20 November 2018

N. J. Kalton
N. J. Kalton*
Affiliation:
University of Missouri, Columbia, Missouri
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Let X be a quasi-Banach space whose dual X* separates the points of X. Then X* is a Banach space under the norm

From X we can construct the Banach envelope Xc of X by defining for x ∊ X, the norm

Then Xc is the completion of (X, ‖ ‖c). Alternatively ‖ ‖c is the Minkowski functional of the convex hull of the unit ball. Xc has the property that any bounded linear operator L:X → Z into a Banach space extends with preservation of norm to an operator .

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 38 , Issue 1 , 01 February 1986 , pp. 65 - 86
Copyright
Copyright © Canadian Mathematical Society 1986

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