Boundedness of sign-preserving charges, regularity, and the completeness of inner product spaces
2005 ◽
Vol 78
(2)
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pp. 199-210
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AbstractWe 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.
2004 ◽
Vol 69
(2)
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pp. 327-340
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2021 ◽
Vol 3
(2)
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pp. 80
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2005 ◽
Vol 2005
(18)
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pp. 2883-2893
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2020 ◽
Vol 57
(4)
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pp. 541-551
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2006 ◽
Vol 4
(1)
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pp. 1-6
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