Non-Commutative Martingale Inequalities
نویسندگان
چکیده
منابع مشابه
Non-commutative Martingale Inequalities
We prove the analogue of the classical Burkholder-Gundy inequalites for noncommutative martingales. As applications we give a characterization for an Ito-Clifford integral to be an L-martingale via its integrand, and then extend the Ito-Clifford integral theory in L, developed by Barnett, Streater and Wilde, to L for all 1 < p < ∞. We include an appendix on the non-commutative analogue of the c...
متن کاملNon - Commutative Martingale Transforms
We prove that non-commutative martingale transforms are of weak type (1, 1). More precisely, there is an absolute constant C such that if M is a semi-finite von Neumann algebra and (Mn)n=1 is an increasing filtration of von Neumann subalgebras of M then for any non-commutative martingale x = (xn) ∞ n=1 in L 1(M), adapted to (Mn)n=1, and any sequence of signs (εn) ∞ n=1, ∥∥∥∥ε1x1 + N ∑ n=2 εn(xn...
متن کاملNon-commutative Nash inequalities
A set of functional inequalities – called Nash inequalities – are introduced and analyzed in the context of quantum Markov process mixing. The basic theory of Nash inequalities is extended to the setting of non-commutative Lp spaces, where their relationship to Poincaré and log-Sobolev inequalities are fleshed out. We prove Nash inequalities for a number of unital reversible semigroups. Boundin...
متن کاملBrascamp-Lieb Inequalities for Non-Commutative Integration
We formulate a non-commutative analog of the Brascamp-Lieb inequality, and prove it in several concrete settings. 2000 Mathematics Subject Classification: 47C15, 15A45, 26D15
متن کامل. O A ] 1 4 M ay 2 00 5 On the best constants in some non - commutative martingale inequalities
We determine the optimal orders for the best constants in the non-commutative Burkholder-Gundy, Doob and Stein inequalities obtained recently in the non-commutative martingale theory. AMS Classification: 46L53, 46L51
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Communications in Mathematical Physics
سال: 1997
ISSN: 0010-3616,1432-0916
DOI: 10.1007/s002200050224