4 citations · 5 across the 2 of their papers we have counts for
7 papers
Gundy's decomposition for non-commutative martingales and applications
Javier Parcet, Narcisse Randrianantoanina
We provide an analogue of Gundy's decomposition for L1-bounded non-commutative martingales. An important difference from the classical case is that for any L1-bounded non-commutati…
A weak-type inequality for non-commutative martingales and applications
Narcisse Randrianantoanina
We prove a weak-type (1,1) inequality for square functions of non-commutative martingales that are simultaneously bounded in and . More precisely, the following non-comm…
Non-commutative martingale transforms
Narcisse Randrianantoanina
We prove that non-commutative martingale transforms are of weak type . More precisely, there is an absolute constant such that if $\M$ is a semi-finite von Neumann algeb…
Embeddings of into non-commutative spaces
Narcisse Randrianantoanina
Let $\M$ be a semi-finite von Neumann algebra equipped with a faithful normal trace . We study the subspace structures of non-commutative Lorentz spaces $L_{p,q}(\M, τ)$, extend…
Compact range property and operators on -algebras
Narcisse Randrianantoanina
We prove that a Banach space has the compact range property (CRP) if and only if for any given -algebra , every absolutely summing operator from into …
Sequences in non-commutative L^p-spaces
Narcisse Randrianantoanina
Let be a semi-finite von Neumann algebra equipped with a distinguished faithful, normal, semi-finite trace . We introduce the notion of equi-integrability in non-commut…