Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



$ q$-Chaos

Authors: Marius Junge and Hun Hee Lee
Journal: Trans. Amer. Math. Soc. 363 (2011), 5223-5249
MSC (2010): Primary 47L25; Secondary 46B07
Published electronically: May 18, 2011
MathSciNet review: 2813414
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Abstract: We consider the $ L_p$ norm estimates for homogeneous polynomials of $ q$-Gaussian variables ( $ -1\leq q\leq 1$). When $ -1<q<1$ the $ L_p$ estimates for $ 1\leq p \leq 2$ are essentially the same as the free case ($ q=0$), whilst the $ L_p$ estimates for $ 2\leq p \leq \infty$ show a strong $ q$-dependence. Moreover, the extremal cases $ q = \pm 1$ produce decisively different formulae.

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Marius Junge
Affiliation: Department of Mathematics, University of Illinois at Urbana-Champaign, 273 Altgeld Hall, 1409 W. Green Street, Urbana, Illinois 61801

Hun Hee Lee
Affiliation: Department of Mathematics, Chungbuk National University, 410 Sungbong-Ro, Heungduk-Gu, Cheongju 361-763, Korea

Keywords: Operator space, quantum probability, $q$-Gaussian, Araki-woods factor, CAR, CCR
Received by editor(s): January 21, 2008
Received by editor(s) in revised form: June 22, 2009, and July 11, 2009
Published electronically: May 18, 2011
Additional Notes: The first author was partially supported by NSF DMS - 0901457
The second author was partially supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2010-0015222)
Article copyright: © Copyright 2011 American Mathematical Society