Abstract:
In the paper, a general method for the construction of bases and unconditional finite-dimensional basis decompositions for spaces with the property of unconditional martingale differences is proposed. The construction makes use of a certain strongly continuous representation of Cantor's group in these spaces. The results are applied to vector function spaces and symmetric spaces of measurable operators associated with factors of type II.
Citation:
F. A. Sukochev, S. V. Ferleger, “Harmonic analysis in (UMD)-spaces: Applications to the theory of bases”, Mat. Zametki, 58:6 (1995), 890–905; Math. Notes, 58:6 (1995), 1315–1326
\Bibitem{SukFer95}
\by F.~A.~Sukochev, S.~V.~Ferleger
\paper Harmonic analysis in (UMD)-spaces: Applications to the theory of bases
\jour Mat. Zametki
\yr 1995
\vol 58
\issue 6
\pages 890--905
\mathnet{http://mi.mathnet.ru/mzm2108}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1382097}
\zmath{https://zbmath.org/?q=an:0857.46006}
\transl
\jour Math. Notes
\yr 1995
\vol 58
\issue 6
\pages 1315--1326
\crossref{https://doi.org/10.1007/BF02304891}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1995UJ43300026}
Linking options:
https://www.mathnet.ru/eng/mzm2108
https://www.mathnet.ru/eng/mzm/v58/i6/p890
This publication is cited in the following 4 articles:
Jinghao Huang, Marat Pliev, Fedor Sukochev, “On Narrow Operators from Lp into Operator Ideals”, Mediterr. J. Math., 19:5 (2022)
Jinghao Huang, Fedor Sukochev, Dmitriy Zanin, “Optimal estimates for martingale transforms”, Journal of Functional Analysis, 282:11 (2022), 109451
M. Caspers, D. Potapov, F. Sukochev, “The Walsh basis in theLp-spaces of hyperfiniteIIIλfactors,0<λ≤1”, Journal of Mathematical Analysis and Applications, 408:1 (2013), 154
P. G. Dodds, S. V. Ferleger, B. de Pagter, F. A. Sukochev, “Vilenkin systems and generalized triangular truncation operator”, Integr equ oper theory, 40:4 (2001), 403