Transformations on the Set of All n-Dimensional Subspaces of a Hilbert Space Preserving Principal Angles |
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Authors: | Lajos Molnár |
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Institution: | Institute of Mathematics and Informatics, University of Debrecen, 4010 Debrecen, P.O.Box 12, Hungary?E-mail: molnarl@math.klte.hu, HU
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Abstract: | Wigner's classical theorem on symmetry transformations plays a fundamental role in quantum mechanics. It can be formulated,
for example, in the following way: Every bijective transformation on the set ℒ of all 1-dimensional subspaces of a Hilbert
space H which preserves the angle between the elements of ℒ is induced by either a unitary or an antiunitary operator on H. The aim of this paper is to extend Wigner's result from the 1-dimensional case to the case of n-dimensional subspaces of H with n∈ℕ fixed.
Received: 28 August 2000 / Accepted: 30 October 2000 |
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