NDLI: Quantum Logic and the Locally Convex Spaces

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Quantum Logic and the Locally Convex Spaces

Content Provider	Scilit
Author	Wilbur, W. John
Copyright Year	1975
Description	An important theorem of Kakutani and Mackey characterizes an infinite dimensional real (complex) Hilbert space as an infinite dimensional real (complex) Banach space whose lattice of closed subspaces admits an orthocomplementation. This result, also valid for quaternionic spaces, has proved useful as a justification for the unique role of Hilbert space in quantum theory. With a like application in mind, we present in the present paper a number of characterizations of real and complex Hilbert space in the class of locally convex spaces. One of these is an extension of the Kakutani-Mackey result from the infinite dimensional Banach spaces to the class of all infinite dimensional complete Mackey spaces. The implications for the foundations of quantum theory are discussed.
Related Links	https://www.ams.org/tran/1975-207-00/S0002-9947-1975-0367607-1/S0002-9947-1975-0367607-1.pdf
Ending Page	360
Page Count	18
Starting Page	343
ISSN	00029947
e-ISSN	10886850
DOI	10.2307/1997181
Journal	Transactions of the American Mathematical Society
Volume Number	207
Language	English
Publisher	Duke University Press
Access Restriction	Open
Subject Keyword	Mathematical Physics Quantum Logic Locally Convex Spaces Logic and the Locally
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics

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