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On isomorphisms of inner product spaces

In: Mathematica Slovaca, vol. 54, no. 2
David Buhagiar - Emanuel Chetcuti
Detaily:
Rok, strany: 2004, 109 - 117
O článku:
In this paper, we show that if $S1$ and $S2$ are two separable, real inner product spaces such that $P(S1)$ is algebraically isomorphic to $P(S2)$, where $P(S)$ denotes the modular lattice of finite and cofinite dimensional subspaces of an inner product space $S$, then $S1$ and $S2$ are isomorphic as inner product spaces. The proof makes use of Gleason's theorem. We also remark that, as a consequence of this, if for two separable, real inner product spaces $S1$, and $S2$, the respective complete lattices of strongly closed subspaces are isomorphic, then $S1$ and $S2$ are unitarily equivalent. In particular, if we just restrict ourselves to complete inner product spaces, we obtain the classical Wigner's theorem ([WIGNER, E. P.: Group Theory and its Applications to Quantum Mechanics of Atomic Spectra, Acad. Press. Inc., New York, 1959]).
Ako citovať:
ISO 690:
Buhagiar, D., Chetcuti, E. 2004. On isomorphisms of inner product spaces. In Mathematica Slovaca, vol. 54, no.2, pp. 109-117. 0139-9918.

APA:
Buhagiar, D., Chetcuti, E. (2004). On isomorphisms of inner product spaces. Mathematica Slovaca, 54(2), 109-117. 0139-9918.