@misc{10481/79289,
year = {2023},
month = {1},
url = {https://hdl.handle.net/10481/79289},
abstract = {We prove that every bijection preserving triple transition pseudoprobabilities
between the sets of minimal tripotents of two atomic JBW
∗
-
triples automatically preserves orthogonality in both directions. Consequently,
each bijection preserving triple transition pseudo-probabilities
between the sets of minimal tripotents of two atomic JBW
∗
-triples is
precisely the restriction of a (complex-)linear triple isomorphism between
the corresponding JBW
∗
-triples. This result can be regarded as triple
version of the celebrated Wigner theorem for Wigner symmetries on the
posets of minimal projections in B(H). We also present a Tingley type
theorem by proving that every surjective isometry between the sets of
minimal tripotents in two atomic JBW
∗
-triples admits an extension to a
real linear surjective isometry between these two JBW
∗
-triples. We also
show that the class of surjective isometries between the sets of minimal
tripotents in two atomic JBW
∗
-triples is, in general, strictly wider than
the set of bijections preserving triple transition pseudo-probabilities.},
organization = {Universidad de Granada/CBUA},
organization = {ERDF/Ministry of Science and Innovation -State Research Agency	PID2021-122126NB-C31},
organization = {Junta de Andalucia	FQM375
PY20 00255},
organization = {IMAG-Maria de Maeztu Grant	CEX2020-001105-M/AEI},
publisher = {Springer},
keywords = {Wigner theorem},
keywords = {Minimal partial isometries},
keywords = {Minimal tripotents},
keywords = {Triple transition pseudo-probability},
keywords = {Preservers},
keywords = {Cartan factors},
keywords = {Surjective isometry},
keywords = {Tingley's type theorem},
title = {Preservers of Triple Transition Pseudo-Probabilities in Connection with Orthogonality Preservers and Surjective Isometries},
doi = {10.1007/s00025-022-01827-w},
author = {Peralta Pereira, Antonio Miguel},
}