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Boundedness of sign-preserving charges, regularity, and the completeness of inner product spaces
Published online by Cambridge University Press: 09 April 2009
Abstract
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We introduce sign-preserving charges on the system of all orthogonally closed subspaces, F(S), of an inner product space S, and we show that it is always bounded on all the finite-dimensional subspaces whenever dim S = ∞. When S is finite-dimensional this is not true. This fact is used for a new completeness criterion showing that S is complete whenever F(S) admits at least one non-zero sign-preserving regular charge. In particular, every such charge is always completely additive.
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- Research Article
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- Copyright © Australian Mathematical Society 2005
References
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