S. V. Astashkin, F. A. Sukochev, “Series of independent mean zero random variables in rearrangement invariant spaces with the Kruglov property”, Investigations on linear operators and function theory. Part 35, Zap. Nauchn. Sem. POMI, 345, POMI, St. Petersburg, 2007, 25–50; J. Math. Sci. (N. Y.), 148:6 (2008), 795

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Zapiski Nauchnykh Seminarov POMI, 2007, Volume 345, Pages 25–50 (Mi znsl95)

This article is cited in 21 scientific papers (total in 21 papers)

Series of independent mean zero random variables in rearrangement invariant spaces with the Kruglov property

S. V. Astashkin^a, F. A. Sukochev^b

^a Samara State University
^b Flinders University

Full-text PDF (305 kB) Citations (21)

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Abstract: This paper compares sequences of independent mean zero random variables in a rearrangement invariant space

X

$X$ on

[0, 1]

$[0,1]$ with sequences of disjoint copies of individual terms in the corresponding rearrangement invariant space

Z_{X}^{2}

$Z_X^2$ on

[0, \infty)

$[0,\infty)$ . Principal results of the paper show that these sequences are equivalent in

X

$X$ and

Z_{X}^{2}

$Z_X^2$ respectively if and only if

X

$X$ possesses the (so-called) Kruglov property. We also apply our technique to complement well-known results concerning isomorphism between rearrangement invariant spaces on

[0, 1]

$[0,1]$ and

[0, \infty)

$[0,\infty)$ .

Received: 09.03.2007

English version:
Journal of Mathematical Sciences (New York), 2008, Volume 148, Issue 6, Pages 795–809
DOI: https://doi.org/10.1007/s10958-008-0026-z

Bibliographic databases:

UDC: 517.5

Language: Russian

Citation: S. V. Astashkin, F. A. Sukochev, “Series of independent mean zero random variables in rearrangement invariant spaces with the Kruglov property”, Investigations on linear operators and function theory. Part 35, Zap. Nauchn. Sem. POMI, 345, POMI, St. Petersburg, 2007, 25–50; J. Math. Sci. (N. Y.), 148:6 (2008), 795–809

Citation in format AMSBIB

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\by S.~V.~Astashkin, F.~A.~Sukochev

\paper Series of independent mean zero random variables in rearrangement invariant spaces with the Kruglov property

\inbook Investigations on linear operators and function theory. Part~35

\serial Zap. Nauchn. Sem. POMI

\yr 2007

\vol 345

\pages 25--50

\publ POMI

\publaddr St.~Petersburg

\mathnet{http://mi.mathnet.ru/znsl95}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2432174}

\elib{https://elibrary.ru/item.asp?id=9595484}

\transl

\jour J. Math. Sci. (N. Y.)

\yr 2008

\vol 148

\issue 6

\pages 795--809

\crossref{https://doi.org/10.1007/s10958-008-0026-z}

\elib{https://elibrary.ru/item.asp?id=13582331}

\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-38549095540}

Linking options:

https://www.mathnet.ru/eng/znsl95

https://www.mathnet.ru/eng/znsl/v345/p25

This publication is cited in the following 21 articles:

S. V. Astashkin, “Sequences of independent functions and structure of rearrangement invariant spaces”, Russian Math. Surveys, 79:3 (2024), 375–457
Sergey V. Astashkin, The Rademacher System in Function Spaces, 2020, 29
Junge M., Sukochev F., Zanin D., “Embeddings of Operator Ideals Into l-P-Spaces on Finite Von Neumann Algebras”, Adv. Math., 312 (2017), 473–546
Jiao Y., Sukochev F., Xie G., Zanin D., “-moment inequalities for independent and freely independent random variables”, J. Funct. Anal., 270:12 (2016), 4558–4596
Astashkin S.V., Sukochev F.A., “Orlicz Sequence Spaces Spanned by Identically Distributed Independent Random Variables in l-P-Spaces”, J. Math. Anal. Appl., 413:1 (2014), 1–19
S. V. Astashkin, “Martingale Rosenthal inequalities in symmetric spaces”, Sb. Math., 205:12 (2014), 1720–1740
Astashkin S., Sukochev F.A., Zanin D., “Disjointification Inequalities in Symmetric Quasi-Banach Spaces and Their Applications”, Pac. J. Math., 270:2 (2014), 257–285
S. V. Astashkin, “On Complementability of Subspaces in Symmetric Spaces with the Kruglov Property”, Funct. Anal. Appl., 47:2 (2013), 148–151
S. V. Astashkin, “On subspaces generated by independent functions in symmetric spaces with Kruglov property”, St. Petersburg Math. J., 25:4 (2014), 513–527
Astashkin S.V., Tikhomirov K.E., “A Probabilistic Version of Rosenthal's Inequality”, Proc. Amer. Math. Soc., 141:10 (2013), 3539–3547
S. V. Astashkin, “Rosenthal type inequalities for martingales in symmetric spaces”, Russian Math. (Iz. VUZ), 56:11 (2012), 52–57
Sukochev F., Zanin D., “Johnson-Schechtman Inequalities in the Free Probability Theory”, J. Funct. Anal., 263:10 (2012), 2921–2948
Astashkin S.V., “Rademacher series and isomorphisms of rearrangement invariant spaces on the finite interval and on the semi-axis”, J. Funct. Anal., 260:1 (2011), 195–207
S. V. Astashkin, K. E. Tikhomirov, “On Probability Analogs of Rosenthal's Inequality”, Math. Notes, 90:5 (2011), 644–650
Astashkin S., Sukochev F., Wong Ch.P., “Disjointification of martingale differences and conditionally independent random variables with some applications”, Studia Math., 205:2 (2011), 171–200
Astashkin S.V., Sukochev F.A., “Symmetric quasi-norms of sums of independent random variables in symmetric function spaces with the Kruglov property”, Israel J. Math., 184:1 (2011), 455–476
S. V. Astashkin, F. A. Sukochev, “Independent functions and the geometry of Banach spaces”, Russian Math. Surveys, 65:6 (2010), 1003–1081
Astashkin S.V., Sukochev F.A., “Best constants in Rosenthal-type inequalities and the Kruglov operator”, Ann. Probab., 38:5 (2010), 1986–2008
S. V. Astashkin, “Rademacher functions in symmetric spaces”, Journal of Mathematical Sciences, 169:6 (2010), 725–886
Sukochev F.A., Zanin D., “Khinchin inequality and Banach–Saks type properties in rearrangement-invariant spaces”, Studia Math., 191:2 (2009), 101–122

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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