Narcisse Randrianantoanina

GUNDY'S DECOMPOSITION FOR NON-COMMUTATIVE MARTINGALES AND APPLICATIONS

We provide an analogue of Gundys decomposition for

A weak type inequality for non-commutative martingales and applications

L_1

Hilbert transform associated with finite maximal subdiagonal algebras

-bounded non-commutative martingales. An important difference from the classical case is that for any

Kadec–Pełczyński decomposition for Haagerup L p -spaces

L_1

Square function inequalities for non-commutative martingales

-bounded non-commutative martingale, the decomposition consists of four martingales. This is strongly related with the row/column nature of non-commutative Hardy spaces of martingales. As applications, we obtain simpler proofs of the weak type

Remarks on James's distortion theorems

(1,1)

Banach Spaces with Complete Continuity Properties

boundedness for non-commutative martingale transforms and the non-commutative analogue of Burkholders weak type inequality for square functions. A sequence

Noncommutative Davis type decompositions and applications: NONCOMMUTATIVE DAVIS TYPE DECOMPOSITIONS AND APPLICATIONS

(x_n)_{n \ge 1}

On complemented versions of James’s distortion theorems

in a normed space

Compact range property and operators on C^*-algebras

\mathrm{X}