| Title:
|
On weakly measurable stochastic processes and absolutely summing operators (English) |
| Author:
|
Marraffa, V. |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
131 |
| Issue:
|
4 |
| Year:
|
2006 |
| Pages:
|
379-391 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
A characterization of absolutely summing operators by means of McShane integrable stochastic processes is considered. (English) |
| Keyword:
|
Pettis integral |
| Keyword:
|
McShane integral |
| Keyword:
|
amart |
| Keyword:
|
uniform amart |
| Keyword:
|
absolutely summing operators |
| MSC:
|
28B05 |
| MSC:
|
46N30 |
| MSC:
|
47B10 |
| MSC:
|
60G48 |
| idZBL:
|
Zbl 1108.60038 |
| idMR:
|
MR2273929 |
| DOI:
|
10.21136/MB.2006.133972 |
| . |
| Date available:
|
2009-09-24T22:27:34Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/133972 |
| . |
| Reference:
|
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| Reference:
|
[2] J. K. Brooks: Representations of weak and strong integrals in Banach spaces.Proc. Nat. Acad. Sci. U.S.A. 63 (1969), 266–279. Zbl 0186.20302, MR 0274697, 10.1073/pnas.63.2.266 |
| Reference:
|
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| Reference:
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[4] G. A. Edgar, L. Sucheston: Stopping Times and Directed Sets.Cambridge University Press, New York, 1992. MR 1191395 |
| Reference:
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[5] L. Egghe: Convergence of adapted sequences of Pettis-integrable functions.Pacific J. Math. 114 (1984), 345–366. Zbl 0514.46028, MR 0757506, 10.2140/pjm.1984.114.345 |
| Reference:
|
[6] D. H. Fremlin: The generalized McShane integral.Illinois J. Math. 39 (1995), 39–67. Zbl 0810.28006, MR 1299648, 10.1215/ijm/1255986628 |
| Reference:
|
[7] N. Ghoussoub: Summability and vector amarts.J. Multivariate Anal. 9 (1979), 173–178. Zbl 0407.60043, MR 0530649, 10.1016/0047-259X(79)90076-9 |
| Reference:
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[8] R. A. Gordon: The McShane integral of Banach-valued functions.Illinois J. Math. 34 (1990), 557–567. Zbl 0685.28003, MR 1053562, 10.1215/ijm/1255988170 |
| Reference:
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[9] Luu Dinh Quang: Convergence of Banach-space-valued martingale-like sequences of Pettis-integrable functions.Bull. Polish Acad. Sci. Math. 45 (1997), 233–245. Zbl 0892.60009, MR 1477541 |
| Reference:
|
[10] V. Marraffa: A characterization of absolutely summing operators by means of McShane integrable functions.J. Math. Anal. Appl. 293/1 (2004), 71–78. Zbl 1087.47023, MR 2052532, 10.1016/j.jmaa.2003.12.029 |
| Reference:
|
[11] V. Marraffa: Stochastic processes of vector valued Pettis and McShane integrable functions.Folia Mathematica 11 (2005). Zbl 1125.60040, MR 2282634 |
| Reference:
|
[12] K. Musial: Martingales of Pettis integrable functions.Lect. Notes Math., Springer 794 (1980), 324–339. Zbl 0433.28010, MR 0577981, 10.1007/BFb0088234 |
| Reference:
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[13] K. Musial: Topics in the theory of Pettis integration.Rend. Istit. Mat. Univ. Trieste 23 (1991), 177–262. Zbl 0798.46042, MR 1248654 |
| Reference:
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[14] J. Rodriguez: Absolutely summig operators and integration of vector-valued functions.J. Math. Anal. Appl. 316 (2006), 579–600. MR 2207332, 10.1016/j.jmaa.2005.05.001 |
| Reference:
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[15] C. Swartz: Beppo Levi’s theorem for vector valued McShane integral and applications.Bull. Belg. Math. Soc. 4 (1997), 589–599. MR 1600292, 10.36045/bbms/1105737762 |
| Reference:
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[16] M. Talagrand: Pettis Integral and Measure Theory.vol. 51, Memoirs A.M.S., 1984. Zbl 0582.46049, MR 0756174 |
| Reference:
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[17] J. J. Uhl, Jr.: Martingales of strongly measurable Pettis integrable functions.Trans. Amer. Math. Soc. 167 (1972), 369–378. Zbl 0249.60025, MR 0293708, 10.1090/S0002-9947-1972-0293708-X |
| . |
