S. V. Astashkin, F. A. Sukochev, “Comparison of Sums of Independent and Disjoint Functions in Symmetric Spaces”, Mat. Zametki, 76:4 (2004), 483–489; Math. Notes, 76:4 (2004), 449

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Matematicheskie Zametki, 2004, Volume 76, Issue 4, Pages 483–489
DOI: https://doi.org/10.4213/mzm122 (Mi mzm122)

This article is cited in 16 scientific papers (total in 16 papers)

Comparison of Sums of Independent and Disjoint Functions in Symmetric Spaces

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

^a Samara State University
^b Flinders University

Full-text PDF (223 kB) Citations (16)

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DOI: https://doi.org/10.4213/mzm122

Abstract: The sums of independent functions (random variables) in a symmetric space

$X$ on

$[0,1]$ are studied. We use the operator approach closely connected with the methods developed, primarily, by Braverman. Our main results concern the Orlicz exponential spaces

$\exp(L_p)$ ,

$1\leqslant p\leqslant\infty$ , and Lorentz spaces

$\Lambda_\psi$ . As a corollary, we obtain results that supplement the well-known Johnson–Schechtman theorem stating that the condition

$L_p\subset X$ ,

$p<\infty$ , implies the equivalence of the norms of sums of independent functions and their disjoint “copies”. In addition, a statement converse, in a certain sense, to this theorem is proved.

Received: 12.03.2004

English version:
Mathematical Notes, 2004, Volume 76, Issue 4, Pages 449–454
DOI: https://doi.org/10.1023/B:MATN.0000043474.00734.ec

Bibliographic databases:

UDC: 517.5+517.982

Language: Russian

Citation: S. V. Astashkin, F. A. Sukochev, “Comparison of Sums of Independent and Disjoint Functions in Symmetric Spaces”, Mat. Zametki, 76:4 (2004), 483–489; Math. Notes, 76:4 (2004), 449–454

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/mzm122

https://doi.org/10.4213/mzm122

https://www.mathnet.ru/eng/mzm/v76/i4/p483

This publication is cited in the following 16 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
Astashkin S.V., Tikhomirov K.E., “A Probabilistic Version of Rosenthal's Inequality”, Proc. Amer. Math. Soc., 141:10 (2013), 3539–3547
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.V., Sukochev F.A., “Symmetric Quasi-Norms of Sums of Independent Random Variables in Symmetric Function Spaces with the Kruglov Property”, Isr. 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
S. V. Astashkin, D. V. Zanin, E. M. Semenov, F. A. Sukochev, “Kruglov Operator and Operators Defined by Random Permutations”, Funct. Anal. Appl., 43:2 (2009), 83–95
S. V. Astashkin, “A Generalized Khintchine Inequality in Rearrangement Invariant Spaces”, Funct. Anal. Appl., 42:2 (2008), 144–147
S. V. Astashkin, “Independent functions in rearrangement invariant spaces and the Kruglov property”, Sb. Math., 199:7 (2008), 945–963
S. V. Astashkin, F. A. Sukochev, “Series of independent mean zero random variables in rearrangement invariant spaces with the Kruglov property”, J. Math. Sci. (N. Y.), 148:6 (2008), 795–809
S. V. Astashkin, F. A. Sukochev, “Sums of independent functions in symmetric spaces with the Kruglov property”, Math. Notes, 80:4 (2006), 593–598
Astashkin S. V., Sukochev F. A., “Series of independent random variables in rearrangement invariant spaces: An operator approach”, Israel J. Math., 145 (2005), 125–156

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

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