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Mark Pankov: Wigner's theorem and its generalizations

Date: 6. 11. 2017
Source: Algebra and functional analysis seminar
Četrtek, 9. 11. 2017, ob 12:30 v predavalnici 2.03, FMF, Jadranska 21, Ljubljana

Vljudno vabljeni!                             

Roman Drnovšek in Primož Moravec

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ABSTRACT: Let $H$ be a complex Hilbert space. The classical Wigner theorem can be formulated as follows: every bijective transformations of the set of pure states (i.e. $1$-dimensional subspaces of $H$) preserving the orthogonality relation in both directions is induced by a unitary or anti-unitary operator. There is also a non-bijective version of this result concerning transformations preserving the angles between pure states.
I describe some extensions of these results to Hilbert Grassmannians.