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Let $A$ be a finite subdiagonal algebra in Arvesons sense. Let $H^p(A)$ be the associated noncommutative Hardy spaces, $0<ple8$. We extend to the case of all positive indices most recent results about these spaces, which include notably the Riesz, Szego and inner-outer type factorizations. One new tool of the paper is the contractivity of the underlying conditional expectation on $H^p(A)$ for $p<1$.
We introduce noncommutative weak Orlicz spaces associated with a weight and study their properties. We also define noncommutative weak Orlicz-Hardy spaces and characterize their dual spaces.
We consider the reduction of problems on general noncommutative $L_p$-spaces to the corresponding ones on those associated with finite von Neumann algebras. The main tool is a unpublished result of the first named author which approximates any noncom
Let $p(cdot): mathbb R^nto(0,infty)$ be a variable exponent function satisfying that there exists a constant $p_0in(0,p_-)$, where $p_-:=mathop{mathrm {ess,inf}}_{xin mathbb R^n}p(x)$, such that the Hardy-Littlewood maximal operator is bounded on the
For a closed cocompact subgroup $Gamma$ of a locally compact group $G$, given a compact abelian subgroup $K$ of $G$ and a homomorphism $rho:hat{K}to G$ satisfying certain conditions, Landstad and Raeburn constructed equivariant noncommutative deforma
For the noncommutative 2-torus, we define and study Fourier transforms arising from representations of states with central supports in the bidual, exhibiting a possibly nontrivial modular structure (i.e. type III representations). We then prove the