Geodesic
On weakly measurable stochastic processes and absolutely summing operators
Mathematica Bohemica, Tome 131 (2006) no. 4, pp. 379-391
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

A characterization of absolutely summing operators by means of McShane integrable stochastic processes is considered.
A characterization of absolutely summing operators by means of McShane integrable stochastic processes is considered.
DOI : 10.21136/MB.2006.133972
Classification : 28B05, 46N30, 47B10, 60G48
Keywords: Pettis integral; McShane integral; amart; uniform amart; absolutely summing operators 
@article{10_21136_MB_2006_133972,
     author = {Marraffa, V.},
     title = {On weakly measurable stochastic processes and absolutely summing operators},
     journal = {Mathematica Bohemica},
     pages = {379--391},
     year = {2006},
     volume = {131},
     number = {4},
     doi = {10.21136/MB.2006.133972},
     mrnumber = {2273929},
     zbl = {1108.60038},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/MB.2006.133972/}
}
TY  - JOUR
AU  - Marraffa, V.
TI  - On weakly measurable stochastic processes and absolutely summing operators
JO  - Mathematica Bohemica
PY  - 2006
SP  - 379
EP  - 391
VL  - 131
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.21136/MB.2006.133972/
DO  - 10.21136/MB.2006.133972
LA  - en
ID  - 10_21136_MB_2006_133972
ER  - 
%0 Journal Article
%A Marraffa, V.
%T On weakly measurable stochastic processes and absolutely summing operators
%J Mathematica Bohemica
%D 2006
%P 379-391
%V 131
%N 4
%U http://geodesic.mathdoc.fr/articles/10.21136/MB.2006.133972/
%R 10.21136/MB.2006.133972
%G en
%F 10_21136_MB_2006_133972
Marraffa, V. On weakly measurable stochastic processes and absolutely summing operators. Mathematica Bohemica, Tome 131 (2006) no. 4, pp. 379-391. doi: 10.21136/MB.2006.133972

[1] A. Bellow: Uniform amarts: a class of asymptotic martingales for which strong almost sure convergence obtains. Z. Wahrscheinlichkeitstheor. Verw. Geb. 41 (1978), 177–191. | DOI | MR | Zbl

[2] J. K. Brooks: Representations of weak and strong integrals in Banach spaces. Proc. Nat. Acad. Sci. U.S.A. 63 (1969), 266–279. | DOI | MR | Zbl

[3] N. Dunford, J. T. Schwartz: Linear Operators. Part I, Interscience, New York, 1958.

[4] G. A. Edgar, L. Sucheston: Stopping Times and Directed Sets. Cambridge University Press, New York, 1992. | MR

[5] L. Egghe: Convergence of adapted sequences of Pettis-integrable functions. Pacific J. Math. 114 (1984), 345–366. | DOI | MR | Zbl

[6] D. H. Fremlin: The generalized McShane integral. Illinois J. Math. 39 (1995), 39–67. | DOI | MR | Zbl

[7] N. Ghoussoub: Summability and vector amarts. J. Multivariate Anal. 9 (1979), 173–178. | DOI | MR | Zbl

[8] R. A. Gordon: The McShane integral of Banach-valued functions. Illinois J. Math. 34 (1990), 557–567. | DOI | MR | Zbl

[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. | MR | Zbl

[10] V. Marraffa: A characterization of absolutely summing operators by means of McShane integrable functions. J. Math. Anal. Appl. 293/1 (2004), 71–78. | DOI | MR | Zbl

[11] V. Marraffa: Stochastic processes of vector valued Pettis and McShane integrable functions. Folia Mathematica 11 (2005). | MR | Zbl

[12] K. Musial: Martingales of Pettis integrable functions. Lect. Notes Math., Springer 794 (1980), 324–339. | DOI | MR | Zbl

[13] K. Musial: Topics in the theory of Pettis integration. Rend. Istit. Mat. Univ. Trieste 23 (1991), 177–262. | MR | Zbl

[14] J. Rodriguez: Absolutely summig operators and integration of vector-valued functions. J. Math. Anal. Appl. 316 (2006), 579–600. | DOI | MR

[15] C. Swartz: Beppo Levi’s theorem for vector valued McShane integral and applications. Bull. Belg. Math. Soc. 4 (1997), 589–599. | DOI | MR

[16] M. Talagrand: Pettis Integral and Measure Theory. vol. 51, Memoirs A.M.S., 1984. | MR | Zbl

[17] J. J. Uhl, Jr.: Martingales of strongly measurable Pettis integrable functions. Trans. Amer. Math. Soc. 167 (1972), 369–378. | DOI | MR | Zbl

Cité par Sources :