Existence of Bade functionals

for complete Boolean algebras

of projections in Fréchet spaces

Author:
W. J. Ricker

Journal:
Proc. Amer. Math. Soc. **125** (1997), 2401-2407

MSC (1991):
Primary 47B15, 46G10, 47C05

DOI:
https://doi.org/10.1090/S0002-9939-97-04028-8

MathSciNet review:
1415365

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Abstract: A classical result of W. Bade states that if is any complete Boolean algebra of projections in an arbitrary Banach space then, for every there exists an element (called a Bade functional for with respect to in the dual space , with the following two properties: (i) is non-negative on and, (ii) whenever satisfies It is shown that a Fréchet space has this property if and only if it does not contain an isomorphic copy of the sequence space

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Additional Information

**W. J. Ricker**

Affiliation:
School of Mathematics, University of New South Wales, Sydney, New South Wales, 2052 Australia

DOI:
https://doi.org/10.1090/S0002-9939-97-04028-8

Received by editor(s):
March 4, 1996

Communicated by:
Palle E. T. Jorgensen

Article copyright:
© Copyright 1997
American Mathematical Society