Geodesic
Linear preservers of equivalence relations on infinite-dimensional spaces
Tatjana Petek 1   ; Gordana Radić 2
1 Faculty of Electrical Engineering and Computer Science University of Maribor Smetanova ul. 17 SI-2000 Maribor, Slovenia and Institute of Mathematics, Physics and Mechanics Jadranska ul. 19 SI-1000 Ljubljana, Slovenia
2 Faculty of Electrical Engineering and Computer Science University of Maribor Smetanova ul. 17 SI-2000 Maribor, Slovenia
Studia Mathematica, Tome 238 (2017) no. 2, pp. 101-119 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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Linear maps preserving equivalence, equivalence by unitaries or congruence, acting on an infinite-dimensional Banach/Hilbert space, are classified. In the first two cases a unified approach is used: we identify the orbit of the identity and show that it is invariant under the map under consideration. Known results on linear invertibility or unitary group preservers are then used.
DOI : 10.4064/sm8356-12-2016
Keywords: linear maps preserving equivalence equivalence unitaries congruence acting infinite dimensional banach hilbert space classified first cases unified approach identify orbit identity invariant under map under consideration known results linear invertibility unitary group preservers

Tatjana Petek  1   ; Gordana Radić  2

1 Faculty of Electrical Engineering and Computer Science University of Maribor Smetanova ul. 17 SI-2000 Maribor, Slovenia and Institute of Mathematics, Physics and Mechanics Jadranska ul. 19 SI-1000 Ljubljana, Slovenia
2 Faculty of Electrical Engineering and Computer Science University of Maribor Smetanova ul. 17 SI-2000 Maribor, Slovenia 
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Tatjana Petek; Gordana Radić. Linear preservers of equivalence relations on infinite-dimensional spaces. Studia Mathematica, Tome 238 (2017) no. 2, pp. 101-119. doi: 10.4064/sm8356-12-2016

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