| Title:
|
Extension theorems (vector measures on quantum logics) (English) |
| Author:
|
Avallone, Anna |
| Author:
|
Hamhalter, Jan |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
46 |
| Issue:
|
1 |
| Year:
|
1996 |
| Pages:
|
179-192 |
| . |
| Category:
|
math |
| . |
| MSC:
|
03G12 |
| MSC:
|
28A60 |
| MSC:
|
28B05 |
| MSC:
|
28B10 |
| MSC:
|
46G10 |
| MSC:
|
46L50 |
| MSC:
|
81P10 |
| idZBL:
|
Zbl 0909.28010 |
| idMR:
|
MR1371699 |
| DOI:
|
10.21136/CMJ.1996.127281 |
| . |
| Date available:
|
2009-09-24T09:55:18Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127281 |
| . |
| Reference:
|
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| Reference:
|
[2] J. Diestel, J.J. Uhl: Vector measure.1977, Math. Surveys n. 15. MR 0453964 |
| Reference:
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[3] N. Dunford, J.T. Schwartz: Linear Operators, Part I.Wiley-Interscience, New York, 1958. MR 1009162 |
| Reference:
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[4] A. Dvurečenskij: Gleason Theorem and its Application.Kluwer Academic Publishers, Dordrecht (Boston), London, 1993. MR 1256736 |
| Reference:
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[5] A. Dvurečenskij, S. Pulmannová: Random measures on a logic.Demonstratio Mathematica 14 (1981), 305–320. MR 0632289 |
| Reference:
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[6] S.P. Gudder: Stochastic Methods in Quantum Mechanics.North Holland, Elsevier, 1979. Zbl 0439.46047, MR 0543489 |
| Reference:
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[7] J. Hamhalter: Orthogonal vector measures on projection lattices in a Hilbert space.Comment. Math. Univ. Carolinae 31 (1990), 655–660. Zbl 0743.46067, MR 1091363 |
| Reference:
|
[8] J. Hamhalter: States on $W^*$-algebras and orthogonal vector measures.Proc. Amer. Math. Soc. 110 (1990), 803-806. Zbl 0743.46063, MR 1036987 |
| Reference:
|
[9] J. Hamhalter: Additivity of vector Gleason measures.Int. J. of Theor. Phys. 31 (1990), 3–13. MR 1142249, 10.1007/BF00674335 |
| Reference:
|
[10] J. Hamhalter: Gleason property and extensions of states on projection logics.Bull. London. Math. Soc. 26, (1994), to appear. Zbl 0830.46055, MR 1302070, 10.1112/blms/26.4.367 |
| Reference:
|
[11] J. Hamhalter, P. Pták: Hilbert space-valued measures on Boolean algebras (extensions).Acta Math. Univ. Comen. LX, 2 (1991), 1-6. MR 1155246 |
| Reference:
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[12] J. Hamhalter, P. Pták: Hilbert space-valued states on quantum logics.Appl. Math. 37 (1992), 51–61. MR 1152157 |
| Reference:
|
[13] R.L. Hudson, S. Pulmannová: Sum logics and tensor products.Foundations of Physics 23 (1993), 999–1024. MR 1237047, 10.1007/BF00736013 |
| Reference:
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[14] R. Jajte: Gleason measures.Prob. Anal. and Related Topics 2 (1979), 69–104. Zbl 0479.46047, MR 0556679 |
| Reference:
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[15] R. V. Kadison, J. R. Ringrose: Fundamentals of the theory of operators algebras Vol. I.Academic Press, Inc., 1986. MR 0859186 |
| Reference:
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[16] Z. Lipecki: Extensions of additive set functions with values in a topological group.Bull. Acad. Pol. Sc. XXII 1 (1974), 19–27. Zbl 0275.28013, MR 0349947 |
| Reference:
|
[17] P. Pták: On extensions of states on logics.Bull. Polish Acad. Sciences Mathematics 9–10 (1985), 493–497. MR 0826375 |
| Reference:
|
[18] P. Pták, S. Pulmannová: Orthomodular Structures as Quantum Logics.Kluwer Academic Publishers, Dordrecht (Boston), London, 1991. MR 1176314 |
| Reference:
|
[19] H. Weber: Valuations on Complemented Lattices.Preprint (1993). Zbl 0843.06005, MR 1353726 |
| Reference:
|
[20] H. Weber: FN-topologies and measures.(1984), Notes on Lessons at University of Naples. |
| . |
