On spectral theory in effect algebras (Q2889982)
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scientific article; zbMATH DE number 6044102
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On spectral theory in effect algebras |
scientific article; zbMATH DE number 6044102 |
Statements
8 June 2012
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Hilbert space
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orthomodular lattice
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orthomodular poset
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effect algebra
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observable
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spectrum
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spectral decomposition
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On spectral theory in effect algebras (English)
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Let \(L\) be the projection lattice of a complex Hilbert space \(H\). Via the spectral theorem, the set of observables can be identified with the self-adjoint operators on \(H\). \textit{D.~E.~Catlin} [``Spectral theory in quantum logics'', Int. J. Theor. Phys. 1, No. 3, 285--297 (1968)] classified the spectra of an observable \(A\) by considering the character of \((A-\lambda\,I)^{-1}\) on a \(\sigma\)-OMP without the aid of Hilbert space formalism. Then he used this classification to prove some spectral mapping theorems. In this paper, the authors extend these results to a \(\sigma\)-effect algebras.
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