On subspaces generated by independent functions in symmetric spaces with Kruglov property
Algebra i analiz, Tome 25 (2013) no. 4, pp. 1-22.

Voir la notice de l'article provenant de la source Math-Net.Ru

@article{AA_2013_25_4_a0,
     author = {S. V. Astashkin},
     title = {On subspaces generated by independent functions in symmetric spaces with {Kruglov} property},
     journal = {Algebra i analiz},
     pages = {1--22},
     publisher = {mathdoc},
     volume = {25},
     number = {4},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AA_2013_25_4_a0/}
}
TY  - JOUR
AU  - S. V. Astashkin
TI  - On subspaces generated by independent functions in symmetric spaces with Kruglov property
JO  - Algebra i analiz
PY  - 2013
SP  - 1
EP  - 22
VL  - 25
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/AA_2013_25_4_a0/
LA  - ru
ID  - AA_2013_25_4_a0
ER  - 
%0 Journal Article
%A S. V. Astashkin
%T On subspaces generated by independent functions in symmetric spaces with Kruglov property
%J Algebra i analiz
%D 2013
%P 1-22
%V 25
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/AA_2013_25_4_a0/
%G ru
%F AA_2013_25_4_a0
S. V. Astashkin. On subspaces generated by independent functions in symmetric spaces with Kruglov property. Algebra i analiz, Tome 25 (2013) no. 4, pp. 1-22. http://geodesic.mathdoc.fr/item/AA_2013_25_4_a0/

[1] Lindenstrauss J., Tzafriri L., Classical Banach spaces, v. II, Function spaces, Springer-Verlag, Berlin–New York, 1979 | MR | Zbl

[2] Johnson W. B., Maurey B., Schechtman G., Tzafriri L., Symmetric structures in Banach spaces, Mem. Amer. Math. Soc., 19, no. 217, 1979, 298 pp. | MR

[3] Kashin B. S., Saakyan A. A., Ortogonalnye ryady, Izd-vo AFTs, M., 1999 | MR | Zbl

[4] Rodin V. A., Semenov E. M., “O dopolnyaemosti podprostranstva, porozhdennogo sistemoi Rademakhera, v simmetrichnom prostranstve”, Funkts. anal. i ego pril., 13:2 (1979), 91–92 | MR | Zbl

[5] Braverman M. Sh., Independent Random Variables and Rearrangement Invariant Spaces, Cambridge Univ. Press, Cambridge, 1994 | MR | Zbl

[6] Braverman M. Sh., “O dopolnyaemosti podprostranstv, porozhdennykh nezavisimymi funktsiyami, v simmetrichnom prostranstve”, Funkts. anal. i ego pril., 16:2 (1982), 66–67 | MR | Zbl

[7] Dor L. E., Starbird T., “Projections of $L_p$ onto subspaces spanned by independent random variables”, Compositio Mathematica, 39:2 (1979), 141–175 | MR | Zbl

[8] Rosenthal H. P., “On the subspaces of $L^p$ ($p>2$) spanned by sequences of independent random variables”, Israel. J. Math., 8 (1970), 273–303 | DOI | MR | Zbl

[9] Johnson W. B., Schechtman G., “Sums of independent random variables in rearrangement invariant function spaces”, Ann. Probab., 17:2 (1989), 789–808 | DOI | MR | Zbl

[10] Astashkin S. V., Sukochev F. A., “Ryady nezavisimykh funktsii s nulevym srednim v simmetrichnykh prostranstvakh so svoistvom Kruglova”, Zap. nauch. semin. POMI, 345, 2006, 25–50 | MR

[11] Astashkin S. V., Sukochev F. A., “Nezavisimye funktsii i geometriya banakhovykh prostranstv”, Uspekhi mat. nauk, 65:6 (2010), 3–86 | DOI | MR | Zbl

[12] Astashkin S. V., “O dopolnyaemosti podprostranstv v simmetrichnykh prostranstvakh so svoistvom Kruglova”, Funkts. anal. i ego pril., 47:2 (2013), 80–84 | DOI | Zbl

[13] Krein S. G., Petunin Yu. I., Semenov E. M., Interpolyatsiya lineinykh operatorov, Nauka, M., 1978 | MR

[14] Kantorovich L. V., Akilov G. P., Funktsionalnyi analiz, Nauka, M., 1977 | MR

[15] Bennett C., Sharpley R., Interpolation of Operators, Acad. Press, Boston, 1988 | MR | Zbl

[16] Kruglov V. M., “Zamechanie k teorii bezgranichno delimykh zakonov”, Teoriya veroyatn. i ee primen., 15:2 (1970), 330–336 | MR | Zbl

[17] Creekmore J., “Type and cotype in Lorentz $L_{p,q}$ spaces”, Indag. Math., 43:2 (1981), 145–152 | MR | Zbl

[18] Kaminska A., Maligranda L., “Order convexity and concavity in Lorentz spaces $\Lambda_{p,w}$, $0

\infty$”, Studia Math., 160:3 (2004), 267–286 | DOI | MR | Zbl

[19] Albiac F., Kalton N. J., Topics in Banach Space Theory, Graduate Texts in Mathematics, 233, Springer, New York, 2006 | MR

[20] Elliott R., Stokhasticheskii analiz i ego prilozheniya, Mir, M., 1986 | MR | Zbl

[21] Vakhaniya N. N., Tarieladze V. I., Chobanyan S. A., Veroyatnostnye raspredeleniya v banakhovykh prostranstvakh, Nauka, M., 1985 | MR | Zbl

[22] Gokhberg I. T., Markus A. S., “Ob ustoichivosti bazisov v banakhovykh i gilbertovykh prostranstvakh”, Izv. AN Mold. SSR, 5 (1962), 17–35 | MR

[23] Figiel T., Johnson W. B., Tzafriri L., “On Banach lattices and spaces having local unconditional structure and applications to Lorentz function spaces”, J. Approximation Theory, 13 (1975), 297–312 | DOI | MR

[24] Carothers N. L., Dilworth S. J., “Geometry of Lorentz spaces via interpolation”, Univ. of Texas Functional Analysis Seminar Longhorn Notes 1985–1986, Longhorn Notes, Univ. Texas, Austin, 1987, 107–134 | MR

[25] Dilworth S. J., “Special Banach lattices and their applications”, Handbook of the geometry of Banach spaces, v. 1, North-Holland, Amsterdam, 2001, 497–532 | DOI | MR

[26] Kadec M. I., Pelczynski A., “Bases, lacunary sequences and complemented subspaces in the spaces $L_p$”, Studia Math., 21 (1962), 161–176 | MR

[27] Bennett G., Dor L. E., Goodman V., Johnson W. B., Newman C. M., “On uncomplemented subspaces of $L_p$, $1

2$”, Israel. J. Math., 26:2 (1977), 178–187 | DOI | MR | Zbl

[28] Lindenstrauss J., Pelczynski A., “Absolutely summing operators in $\mathcal L_p$ spaces and their applications”, Studia Math., 29 (1968), 275–326 | MR | Zbl

[29] Tzafriri L., “Uniqueness of structure in Banach spaces”, Handbook of the geometry of Banach spaces, v. 2, North-Holland, Amsterdam, 2003, 1635–1669 | DOI | MR | Zbl

[30] Dor L. E., “On proections in $L_1$”, Ann. of Math. (2), 102:3 (1975), 463–474 | DOI | MR | Zbl

[31] Hernandez F. L., Semenov E. M., “Subspaces generated by translations in rearrangement invariant spaces”, J. Funct. Anal., 169:1 (1999), 52–80 | DOI | MR | Zbl