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States on Subspaces of Inner Product Spaces with the Gleason Property |
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| Authors: | Anatolij Dvurečenskij |
| Institution: | (1) Slovak Academy of Sciences, Mathematical Institute,  tefánikova 49, SK-814 73 Bratislava, Slovakia |
| Abstract: | We show that the range of every finitely additive state on the system
of all orthogonally closed subspaces of an infinite-dimensional inner product space E satisfying the Gleason property is equal to the real interval 0, 1]. Every pre-Hilbert space satisfies the Gleason property, and in Keller spaces it fails to hold. |
| Keywords: | inner product space orthogonally closed subspace finitely additive state range of a state Hilbert space Keller space |
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