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@article{967840,
author = {Paseka, Jan},
article_location = {NEW YORK},
article_number = {4},
doi = {http://dx.doi.org/10.1007/s10773-010-0594-9},
keywords = {(Generalized) effect algebra; Partially ordered commutative group; Hilbert space; (Unbounded) linear operators; PT-symmetry; Pseudo-Hermitian quantum mechanics},
language = {eng},
issn = {0020-7748},
journal = {International Journal of Theoretical Physics},
title = {PT-Symmetry in (Generalized) Effect Algebras},
url = {http://www.springerlink.com/content/88684020j5t72x12/},
volume = {50},
year = {2011}
}
TY - JOUR
ID - 967840
AU - Paseka, Jan
PY - 2011
TI - PT-Symmetry in (Generalized) Effect Algebras
JF - International Journal of Theoretical Physics
VL - 50
IS - 4
SP - 1198-1205
EP - 1198-1205
SN - 00207748
KW - (Generalized) effect algebra
KW - Partially ordered commutative group
KW - Hilbert space
KW - (Unbounded) linear operators
KW - PT-symmetry
KW - Pseudo-Hermitian quantum mechanics
UR - http://www.springerlink.com/content/88684020j5t72x12/
L2 - http://www.springerlink.com/content/88684020j5t72x12/
N2 - We show that an eta (+)-pseudo-Hermitian operator for some metric operator eta (+) of a quantum system described by a Hilbert space H yields an isomorphism between the partially ordered commutative group of linear maps on H and the partially ordered commutative group of linear maps on H(p+). The same applies to the generalized effect algebras of positive operators and to the effect algebras of c-bounded positive operators on the respective Hilbert spaces H and H(p+). Hence, from the standpoint of (generalized) effect algebra theory both representations of our quantum system coincide.
ER -
PASEKA, Jan. PT-Symmetry in (Generalized) Effect Algebras. \textit{International Journal of Theoretical Physics}. NEW YORK, 2011, vol.~50, No~4, p.~1198-1205. ISSN~0020-7748. Available from: https://dx.doi.org/10.1007/s10773-010-0594-9.
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