Maps on Grassmann spaces preserving the minimal principal angle

DOI10.1007/S44146-023-00093-8arXiv2305.18982MaRDI QIDQ6438488

Peter Šemrl

Publication date: 30 May 2023

Abstract: Let $n$ be a positive integer and $H$ a Hilbert space. The description of the general form of bijective maps on the set of $n$-dimensional subspaces of $H$ preserving the maximal principal angle has been obtained recently. This is a generalization of Wigner's unitary-antiunitary theorem. In this paper we will obtain another extension of Wigner's theorem in which the maximal principal angle is replaced by the minimal one. Moreover, in this case we do not need the bijectivity assumption.

Mathematics Subject Classification ID

Transformers, preservers (linear operators on spaces of linear operators) (47B49)

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