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The Strong ϕ Topology on Symmetric Sequence Spaces

Published online by Cambridge University Press:  20 November 2018

William H. Ruckle
William H. Ruckle*
Affiliation:
Clemson University, Clemson, South Carolina
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The strong ϕ topology. Let S be a linear space of real sequences written in functional notation

There is a natural duality between S and the space ϕ of sequences which are eventually ϕ given by the equation

The series has only a finite number of nonzero terms since t is in ϕ.

A subset B of ϕ is called S-bounded if

for each s in S.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 37 , Issue 6 , 01 December 1985 , pp. 1112 - 1133
Copyright
Copyright © Canadian Mathematical Society 1985

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