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Partial inner product spaces: Some categorical aspects

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Antoine, Jean-Pierre [UCL] Lambert, Dominique [FUNDP] Trapani, Camillo [Università di Palermo]

We make explicit in terms of categories a number of statements from the theory of partial inner product spaces (PIP spaces) and operators on them. In particular, we construct sheaves and cosheaves of operators on certain PIP spaces s of practical interest.

Document type Article de périodique (Journal article)
Access type Accès libre
Publication date 2011
Language Anglais
Journal information "Advances in Mathematical Physics" - Vol. 2011, p. Article ID 957592 (22 pages)
Peer reviewed yes
Publisher Hindawi Publishing Corporation ((United States) New York)
issn 1687-9120
e-issn 1687-9139
Publication status Publié
Affiliations UCL - SST/IRMP - Institut de recherche en mathématique et physique
FUNDP - LET_Philosophie
Università di Palermo - Dept. Mathematics
Links
  1. Antoine J.-P, Grossmann A, Partial inner product spaces. I. General properties, 10.1016/0022-1236(76)90063-x
  2. Antoine J.-P, Grossmann A, Partial inner product spaces. II. Operators, 10.1016/0022-1236(76)90064-1
  3. Antoine J.‐P., Partial inner product spaces. III. Compatibility relations revisited, 10.1063/1.524410
  4. Antoine J.‐P., Partial inner product spaces. IV. Topological considerations, 10.1063/1.524717
  5. Antoine Jean-Pierre, Trapani Camillo, Partial Inner Product Spaces, ISBN:9783642051357, 10.1007/978-3-642-05136-4
  6. Antoine Jean-Pierre, Trapani Camillo, The Partial Inner Product Space Method: A Quick Overview, 10.1155/2010/457635
  7. (1997)
  8. (1992)
  9. 345, 349 (2007)
  10. Dörfler Monika, Feichtinger Hans G., Gröchenig Karlheinz, Time-frequency partitions for the Gelfand triple $(S_0,L^2,S_0')$, 10.7146/math.scand.a-14985
  11. (1992)
  12. Closed set sheaves and their categories, 115 (1995)
  13. McKinsey J. C. C., Tarski Alfred, On Closed Elements in Closure Algebras, 10.2307/1969038
  14. Majid Shahn, Foundations of Quantum Group Theory, ISBN:9780511613104, 10.1017/cbo9780511613104
  15. Quantum spacetime and physical reality, 56 (2008)
  16. Bellomonte Giorgia, Trapani Camillo, Rigged Hilbert spaces and contractive families of Hilbert spaces, 10.1007/s00605-010-0249-1
  17. Mityagin B S, Shvarts A S, FUNCTORS IN CATEGORIES OF BANACH SPACES, 10.1070/rm1964v019n02abeh001146
  18. Bulletin de l'Académie Polonaise des Sciences, Série des Sciences Mathématiques, Astronomiques et Physiques, 13, 579 (1965)
  19. (1966)
  20. (1969)
  21. (1990)
Bibliographic reference Antoine, Jean-Pierre ; Lambert, Dominique ; Trapani, Camillo. Partial inner product spaces: Some categorical aspects. In: Advances in Mathematical Physics, Vol. 2011, p. Article ID 957592 (22 pages)
Permanent URL http://hdl.handle.net/2078.1/107585