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Metric Operators, Generalized Hermiticity and Lattices of Hilbert Spaces

Bibliographic reference Antoine, Jean-Pierre ; Trapani, Camillo. Metric Operators, Generalized Hermiticity and Lattices of Hilbert Spaces. In: F. Bagarello, J-P. Gazeau, F. H. Szafraniec and M. Znojil (eds.), Non-Selfadjoint Operators in Quantum Physics: Mathematical Aspects, J.Wiley and Sons  : Hoboken, NJ 2015, p.pp. 345-402
Permanent URL http://hdl.handle.net/2078.1/150941
  1. Bender Carl M, Making sense of non-Hermitian Hamiltonians, 10.1088/0034-4885/70/6/r03
  2. Bender Carl, Fring Andreas, Günther Uwe, Jones Hugh, Quantum physics with non-Hermitian operators, 10.1088/1751-8113/45/44/440301
  3. Bender C. M., DeKieviet M., Klevansky S. P., PT quantum mechanics, 10.1098/rsta.2012.0523
  4. Dieudonné, Proceedings of the International Symposium on Linear Spaces, Jerusalem 1960, 115 (1961)
  5. MOSTAFAZADEH ALI, PSEUDO-HERMITIAN REPRESENTATION OF QUANTUM MECHANICS, 10.1142/s0219887810004816
  6. Siegl P., Krejčiřík D., On the metric operator for the imaginary cubic oscillator, 10.1103/physrevd.86.121702
  7. Bagarello, Phys Rev A, 88, 032120 (2013)
  8. Bagarello Fabio, Fring Andreas, Non-self-adjoint model of a two-dimensional noncommutative space with an unbound metric, 10.1103/physreva.88.042119
  9. Bagarello Fabio, Znojil Miloslav, Nonlinear pseudo-bosons versus hidden Hermiticity: II. The case of unbounded operators, 10.1088/1751-8113/45/11/115311
  10. Mostafazadeh A., Pseudo-Hermitian quantum mechanics with unbounded metric operators, 10.1098/rsta.2012.0050
  11. Antoine Jean-Pierre, Trapani C, Partial inner product spaces, metric operators and generalized hermiticity, 10.1088/1751-8113/46/2/025204
  12. Antoine Jean-Pierre, Trapani Camillo, Some remarks on quasi-Hermitian operators, 10.1063/1.4853815
  13. Antoine Jean-Pierre, Trapani Camillo, Partial Inner Product Spaces, ISBN:9783642051357, 10.1007/978-3-642-05136-4
  14. Hoover, Illinois J Math, 16, 678 (1972)
  15. Dunford Nelson, A survey of the theory of spectral operators, 10.1090/s0002-9904-1958-10219-0
  16. Kantorovitz Shmuel, On the characterization of spectral operators, 10.1090/s0002-9947-1964-0160115-5
  17. Scholtz F.G., Geyer H.B., Hahne F.J.W., Quasi-Hermitian operators in quantum mechanics and the variational principle, 10.1016/0003-4916(92)90284-s
  18. Geyer HB Heiss WD Scholtz FG Non-Hermitian Hamiltonians, metric, other observables and physical implications 2007
  19. Kretschmer R., Szymanowski L., Quasi-Hermiticity in infinite-dimensional Hilbert spaces, 10.1016/j.physleta.2004.03.044
  20. Albeverio S, Günther U, Kuzhel S, J-self-adjoint operators with \mathcal{C} -symmetries: an extension theory approach, 10.1088/1751-8113/42/10/105205
  21. Bognár János, Indefinite Inner Product Spaces, ISBN:9783642655692, 10.1007/978-3-642-65567-8
  22. Kuzhel, Modern Analysis and Applications. The Mark Krein Centenary Conference, 1, 375 (2009)
  23. Bender Carl M, Kuzhel Sergii, Unbounded $\mathcal {C}$-symmetries and their nonuniqueness, 10.1088/1751-8113/45/44/444005
  24. Davies E. Brian, Linear Operators and their Spectra, ISBN:9780511618864, 10.1017/cbo9780511618864
  25. Dunford, Linear Operators. Part I: General Theory; Part II: Spectral Theory (1957)
  26. Reed, Methods of Modern Mathematical Physics. I. Functional Analysis (1972)
  27. Schmüdgen Konrad, Unbounded Self-adjoint Operators on Hilbert Space, ISBN:9789400747524, 10.1007/978-94-007-4753-1
  28. Reed, Methods of Modern Mathematical Physics. IV. Analysis of Operators (1978)
  29. Williams James P., Operators similar to their adjoints, 10.1090/s0002-9939-1969-0233230-5
  30. Sz-Nagy, Harmonic Analysis of Operators in Hilbert Space (1970)
  31. Tzafriri L., Quasi-similarity for spectral operators on Banach spaces, 10.2140/pjm.1968.25.197
  32. Feldzamen, Trans Amer Math Soc, 100, 277 (1961)
  33. �ta Sch�ichi, Schm�dgen Konrad, On some classes of unbounded operators, 10.1007/bf01195114
  34. Davies E.B., Semi-Classical States for Non-Self-Adjoint Schrödinger Operators, 10.1007/s002200050521
  35. Samsonov B. F., Hermitian Hamiltonian equivalent to a given non-Hermitian one: manifestation of spectral singularity, 10.1098/rsta.2012.0044
  36. Bergh Jöran, Löfström Jörgen, Interpolation Spaces, ISBN:9783642664533, 10.1007/978-3-642-66451-9
  37. Ali S. Twareque, Bagarello F., Gazeau Jean Pierre, Modified Landau levels, damped harmonic oscillator, and two-dimensional pseudo-bosons, 10.1063/1.3514196
  38. Antoine J.-P., Balazs P., Frames, Semi-Frames, and Hilbert Scales, 10.1080/01630563.2012.682128
  39. Znojil, Symmetry Integrability and Geom. Methods Appl. (SIGMA), 5, 001 (2009)
  40. Weidmann Joachim, Linear Operators in Hilbert Spaces, ISBN:9781461260295, 10.1007/978-1-4612-6027-1
  41. Inoue Atsushi, Trapani Camillo, Non-Self-Adjoint Resolutions of the Identity and Associated Operators, 10.1007/s11785-014-0359-1
  42. Mackey, Commutative Banach Algebras (1959)
  43. Burnap C., Zweifel P. F., A note on the spectral theorem, 10.1007/bf01199348
  44. Bagarello F., Inoue A., Trapani C., Non-self-adjoint hamiltonians defined by Riesz bases, 10.1063/1.4866779
  45. Christensen Ole, An Introduction to Frames and Riesz Bases, ISBN:9781461265009, 10.1007/978-0-8176-8224-8
  46. Young, An Introduction to Nonharmonic Fourier Series (1980)
  47. Bagarello F., From self-adjoint to non-self-adjoint harmonic oscillators: Physical consequences and mathematical pitfalls, 10.1103/physreva.88.032120
  48. Kadison, Fundamentals of the Theory of Operator Algebras (1983)
  49. Antoine J.‐P., Karwowski W., Interpolation theory and refinement of nested Hilbert spaces, 10.1063/1.524810
  50. Kato Tosio, Perturbation Theory for Linear Operators, ISBN:9783540586616, 10.1007/978-3-642-66282-9
  51. Gitman D.M., Tyutin I.V., Voronov B.L., Self-adjoint Extensions in Quantum Mechanics, ISBN:9780817644000, 10.1007/978-0-8176-4662-2
  52. Barut, Theory of Group Representations and Applications (1977)
  53. Nelson Edward, Analytic Vectors, 10.2307/1970331
  54. Schwartz Jack, Some non-selfadjoint operators, 10.1002/cpa.3160130405
  55. Antoine J-P Trapani C Operators on partial inner product spaces: towards a spectral analysis 2014 Mediterr J Math
  56. Bellomonte Giorgia, Di Bella Salvatore, Trapani Camillo, Operators in rigged Hilbert spaces: Some spectral properties, 10.1016/j.jmaa.2013.10.025
  57. Antoine Jean-Pierre, Trapani Camillo, The Partial Inner Product Space Method: A Quick Overview, 10.1155/2010/457635
  58. Birkhoff, Lattice Theory (1966)
  59. Köthe, Topological Vector Spaces (1969)
  60. Bellomonte Giorgia, Trapani Camillo, Rigged Hilbert spaces and contractive families of Hilbert spaces, 10.1007/s00605-010-0249-1
  61. Mityagin B S, Shvarts A S, FUNCTORS IN CATEGORIES OF BANACH SPACES, 10.1070/rm1964v019n02abeh001146
  62. Semadeni, Bull Acad Polon Sci Sér Sci Math Astr Phys, 13, 579 (1965)
  63. Dieudonné Jean, Sur les espaces de Köthe, 10.1007/bf02790084
  64. Goes Sigrun, Welland Robert, Some remarks on K�the spaces, 10.1007/bf01418768
  65. Antoine Jean-Pierre, Lambert Dominique, Trapani Camillo, Partial Inner Product Spaces: Some Categorical Aspects, 10.1155/2011/957592
  66. Antoine Jean-Pierre, Trapani Camillo, Some Classes of Operators on Partial Inner Product Spaces, Spectral Theory, Mathematical System Theory, Evolution Equations, Differential and Difference Equations (2012) ISBN:9783034802963 p.25-46, 10.1007/978-3-0348-0297-0_3