Hostname: page-component-8448b6f56d-xtgtn Total loading time: 0 Render date: 2024-04-24T08:09:15.702Z Has data issue: false hasContentIssue false

The Hahn-Schur Theorem on effect algebras

Published online by Cambridge University Press:  17 April 2009

A. Aizpuru
Affiliation:
Departamento de Matemáticas, Universidad de Cádiz, Apdo. 40, 11510–Puerto Real (Cádiz), Spain, e-mail: antonio.aizpuru@uca.es, marina.nicasio@uca.es, monserrat.tamayorivera@alum.uca.es
M. Nicasio-Llach
Affiliation:
Departamento de Matemáticas, Universidad de Cádiz, Apdo. 40, 11510–Puerto Real (Cádiz), Spain, e-mail: antonio.aizpuru@uca.es, marina.nicasio@uca.es, monserrat.tamayorivera@alum.uca.es
M. Tamayo
Affiliation:
Departamento de Matemáticas, Universidad de Cádiz, Apdo. 40, 11510–Puerto Real (Cádiz), Spain, e-mail: antonio.aizpuru@uca.es, marina.nicasio@uca.es, monserrat.tamayorivera@alum.uca.es
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper we obtain new results on the uniform convergence on matrices and a new version of the matrix theorem of the Hahn-Schur summation theorem in effect algebras.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 2007

References

[1]Aizpuru, A. and Gutiérrez-Dávila, A., ‘Unconditionally Cauchy series and uniform convergence on Matrices’, Chinese Ann. Math. Ser. B 25 (2004), 335346.CrossRefGoogle Scholar
[2]Aizpuru, A. and Gutiérrez-Dávila, A., ‘On the interchange of series and applications’, Bull. Belg. Math. Soc. 11 (2004), 409430.Google Scholar
[3]Aizpuru, A., Gutiérrez-Dávila, A. and Wu, J., ‘Measures defined on quantum logics of sets’, Internat. J. Theoret. Phys. 44 (2005), 14511458.CrossRefGoogle Scholar
[4]Aizpuru, A. and Tamayo, M., ‘Classical properties of measure theory on effect algebras’, Fuzzy Sets and Systems 157 (2006), 21392143.Google Scholar
[5]Aizpuru, A. and Tamayo, M., ‘Matrix convergence theorems in quantum logics’, (preprint).Google Scholar
[6]Antosik, P. and Swartz, C., Matrix methods in analysis, Lecture Notes in Mathematics 1113 (Springer-Verlag, Berlin, 1985).CrossRefGoogle Scholar
[7]Bennett, M.K. and Foulis, D.J., ‘Effect algebras and unsharp quantum logics’, Found. Phys. 24 (1994), 13311352.Google Scholar
[8]Bennett, M.K. and Foulis, D.J., ‘Interval and scale effect algebras’, Adv. in Appl. Math. 19 (1997), 200215.CrossRefGoogle Scholar
[9]Birkhoff, M.K., Lattice theory 25, Colloquium New York (American Mathematical Society, 1948).Google Scholar
[10]Birkhoff, M.K. and Von Neumann, J., ‘The logic of quantum mechanics’, Ann. Math. 37 (1936), 823843.CrossRefGoogle Scholar
[11]Gudder, S., Quantum probability (Academic Press, London, New York, 1988).Google Scholar
[12]Mazario, F.G., ‘Convergence theorems for topological group valued measures on effect algebras’, Bull. Austral. Math. Soc. 64 (2001), 213231.CrossRefGoogle Scholar
[13]Riecanova, Z., ‘Subalgebras, intervals and Central elements of generalized effect algebras’, Internat. J. Theoret. Phys. 38 (1994), 32043220.Google Scholar
[14]Wu, J., Lu, S. and Kim, D., ‘Antosik-Mikusinski Matrix convergence theorem in quantum logics’, Internat. J. Theoret. Phys. 42 (2003), 19051911.CrossRefGoogle Scholar
[15]Wu, J., Lu, S. and Chu, M., ‘Quantum-logics-valued measure convergence theorem’, Internat. J. Theoret. Phys 42 (2003), 26032608.Google Scholar
[16]Wu, J. and Ma, Z., ‘The Brooks-Jewett theorem on effect algebras with the sequential completeness property’, Czechoslovak J. Phys. 53 (2003), 379383.Google Scholar