On Quantales and Spectra of C*-Algebras

Applied Categorical Structures

Volumn 11, Issue 6, 2003, Pages 543-560

  Kruml, David ^a   Pelletier, Joan Wick ^b   Resende, Pedro ^c   Rosický, Jiří ^a  

^a MASARYK UNIVERSITY   (Czech Republic)

^b YORK UNIVERSITY   (Canada)

^c INSTITUTO SUPERIOR TÉCNICO   (Portugal)

Author keywords

C* algebra; Noncommutative space; Noncommutative spectrum; Spatial quantale

Indexed keywords

FUNCTIONS; SET THEORY; THEOREM PROVING; TOPOLOGY;

NONCOMMUTATIVE SPECTRUM; SPATIAL QUANTALE;

BOOLEAN ALGEBRA;

EID: 0242443822     PISSN: 09272852     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1026106305210     Document Type: Article

References (26)

1. Akemann, C. A.: Left ideal structure of C*-algebras, Journal of Functional Analysis 6 (1970), 305-317.
2. Akemann, C. A.: A Gelfand representation theory for C*-algebras, Pacific Journal of Mathematics 39 (1971), 1-11.
3. Banaschewski, B. and Mulvey, C. J.: The spectral theory of commutative C*-algebras: The constructive spectrum, Quaestiones Mathematicae 23 (2000), 425-464.
4. Banaschewski, B. and Mulvey, C. J.: The spectral theory of commutative C*-algebras: The constructive Gelfand-Mazur theorem, Quaestiones Mathematicae 23 (2000), 465-488.
5. Borceux, F., Rosický, J. and Van den Bossche, G.: Quantales and C*-algebras, The Journal of the London Mathematical Society 40 (1989), 398-404.
6. Borceux, F. and Van den Bossche, G.: Quantales and their sheaves, Order 3 (1986), 61-87.
7. Borceux, F. and Van den Bossche, G.: An essay on noncommutative topology, Topology and its Applications 31 (1989), 203-223.
8. Connes, A.: Noncommutative Geometry, Academic Press, 1994.
9. Giles, R. and Kummer, H.: A non-commutative generalization of topology, Indiana University Mathematics Journal 21 (1971), 91-102.
10. Johnstone, P.: Stone Spaces, Cambridge Stud. Adv. Math. 3, Cambridge Univ. Press, 1982.
11. Kruml, D.: Spatial quantales, Applied Categoriocal Structures 10 (2002), 49-62.
12. Mulvey, C. J.: Rendiconti del Circolo Matematico di Palermo (2) Suppl. (1986), 99-104.
13. Mulvey, C. J.: Quantales, Invited Lecture, Summer Conference on Locales and Topological Groups, Curaçao, 1989.
14. Mulvey, C. J. and Pelletier, J. W.: On the quantisation of spaces, Journal of Pure and Applied Algebra 175 (2002), 289-325.
15. Mulvey, C. J. and Pelletier, J. W.: On the quantisation of points, Journal of Pure and Applied Algebra 159 (2001), 231-295.
16. Mulvey, C. J. and Pelletier, J. W.: A quantisation of the calculus of relations, Canadian Mathematical Society Conference Proceedings 13 (1992), 345-360.
17. Paseka, J.: Simple quantales, in Proc. 8th Prague Topological Symposium 1996, Topology Atlas, 1997.
18. Paseka, J. and Rosický, J.: Quantales, in B. Coecke, D. Moore and A. Wilce (eds), Current Research in Operational Quantum Logic: Algebras, Categories and Languages, Fund. Theories Phys., Vol. 111, Kluwer Academic Publishers, 2000, pp. 245-262.
19. Pelletier, J. W.: Von Neumann algebras and Hilbert quantales, Applied Categorical Structures 5 (1997), 249-264.
20. Pelletier, J. W. and Rosicky, J.: Simple involutive quantales, J. Algebra 195 (1997), 367-386.
21. Resende, P.: Tropological systems are points of quantales, Journal of Pure and Applied Algebra 173 (2002), 87-120.
22. Resende, P.: From algebras to quantales and back, Talk at the Workshop on Categorical Structures for Descent and Galois Theory, Hopf Algebras and Semiabelian Categories, Fields Institute, Toronto, September 23-28, 2002, http://www.fields.utoronto.ca/programs/scientific/0203/galois_and_hopf/.
23. Rieffel, M. A.: Morita equivalence for C*-algebras and W*-algebras, Journal of Pure and Applied Algebra 5 (1974), 51-96.
24. Rosenthal, K.: Quantales and Their Applications, Pitman Res. Notes Math. Ser. 234, Longman Scientific & Technical, Harlow, 1990.
25. Rosický, J.: Characterizing spatial quantales, Algebra Universalis 34 (1995), 175-178.
26. Rosický, J.: Multiplicative lattices and C*-algebras, Cahiers de Topologie et Géométrie Différentielle Catégoriques XXX (1989), 95-110.