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 -