TY - CHAP
T1 - Operator (Quasi-)Similarity, Quasi-Hermitian Operators and All that
AU - Trapani, Camillo
AU - Antoine, Jean-Pierre
PY - 2016
Y1 - 2016
N2 - Motivated by the recent developments of pseudo-Hermitian quantum mechanics,we analyze the structure generated by unbounded metric operators in a Hilbertspace. To that effect, we consider the notions of similarity and quasi-similarity betweenoperators and explore to what extent they preserve spectral properties. Thenwe study quasi-Hermitian operators, bounded or not, that is, operators that are quasisimilarto their adjoint and we discuss their application in pseudo-Hermitian quantummechanics. Finally, we extend the analysis to operators in a partial inner productspace (PIP-space), in particular the scale of Hilbert spaces generated by a single unboundedmetric operator.
AB - Motivated by the recent developments of pseudo-Hermitian quantum mechanics,we analyze the structure generated by unbounded metric operators in a Hilbertspace. To that effect, we consider the notions of similarity and quasi-similarity betweenoperators and explore to what extent they preserve spectral properties. Thenwe study quasi-Hermitian operators, bounded or not, that is, operators that are quasisimilarto their adjoint and we discuss their application in pseudo-Hermitian quantummechanics. Finally, we extend the analysis to operators in a partial inner productspace (PIP-space), in particular the scale of Hilbert spaces generated by a single unboundedmetric operator.
UR - http://hdl.handle.net/10447/183572
M3 - Chapter
SN - 978-3-319-31354-2
T3 - SPRINGER PROCEEDINGS IN PHYSICS
SP - 45
EP - 65
BT - Non-Hermitian Hamiltonians in Quantum Physics
ER -