Searcharxiv⌕ Search

arXiv subjects

Turdebek N. Bekjan

Publications and source records attributed to Turdebek N. Bekjan.

14 recordsLinked to original sources
arXiv2024

On Haagerup noncommutative quasi $H^p(\A)$ spaces

Let $\mathcal{M}$ be a $σ$-finite von Neumann algebra, equipped with a normal faithful state $φ$, and let $\mathcal{A}$ be a maximal subdiagonal subalgebra of $\mathcal{M}$. We have proved that for $0< p<1$, $H^p(\mathcal{A})$ is independent of $φ$. Furthermore, in the case that $\mathcal{A}$ is a type 1 subdiagonal subalgebra, we have extended the most recent results about the Riesz type factorization to the case $0<p<1$ and have proved an interpolation theorem for $H^p(\mathcal{A})$ in the case where $0 < p_0, p_1 \le \infty$.

math.OA↗
arXiv2023

Interpolation of Haagerup noncommutative Hardy spaces

Let $\mathcal{M}$ be a $σ$-finite von Neumann algebra, equipped with a normal faithful state $φ$, and let $\mathcal{A}$ be maximal subdiagonal algebra of $\mathcal{M}$. We prove Stein-Weiss type interpolation theorem of Haagerup noncommutative $H^{p}$-spaces associated with $\A$.

math.OA↗
arXiv2022

Haagerup noncommutative Orlicz spaces

Let $\mathcal{M}$ be a $σ$-finite von Neumann algebra equipped with a normal faithful state $φ$, and let $Φ$ be a growth function. We consider Haagerup noncommutative Orlicz spaces $L^Φ(\M,φ)$ associated with $\M$ and $φ$, which are analogues of Haagerup $L^p$-spaces. We show that $L^Φ(\M,φ)$ is independent of $φ$ up to isometric isomorphism. We prove the Haagerup's reduction theorem and the duality theorem for this spaces. As application of these results, we extend some noncommutative martingale inequalities in the tracial case to the Haagerup noncommutative Orlicz space case.

math.OA↗
arXiv2021

On noncommutative weak Orlicz-Hardy spaces

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.

math.OA↗
arXiv2021

A Beurling-Blecher-Labuschagne theorem for Haagerup noncommutative $L^p$ spaces

Let $\mathcal{M}$ be a $σ$-finite von Neumann algebra, equipped with a normal faithful state $φ$, and let $\mathcal{A}$ be maximal subdiagonal subalgebra of $\mathcal{M}$ and $1\le p<\8$. We prove a Beurling-Blecher-Labuschagne type theorem for $\mathcal{A}$-invariant subspaces of Haagerup noncommutative $L^p(\mathcal{M})$ and give a characterization of outer operators in Haagerup noncommutative $H^{p}$-spaces associated with $\mathcal{A}$.

math.OA↗
arXiv2021

On pointwise products of symmetric quasi Banach spaces and applications

Let $E_1,\;E_2$ be symmetric quasi Banach function spaces on $(0,α)\;(0<α\le\8)$. We study some properties of several constructions (the products $E_1(\M)\odot E_2(\M)$, the Calder$\rm\acute{o}$n spaces $E_1(\M)^θE_2(\M)^{1-θ}$, the complex interpolation spaces $(E_1(\M),E_2(\M))_θ$, the real interpolation method $(E_1(\M),E_2(\M))_{θ,p}$) in the context of noncommutative symmetric quasi Banach spaces. Under some natural assumptions, we prove $$ (E_1(\M), E_2(\M))_θ=E_1(\M)^θE_2(\M)^{1-θ}=E_1^{(\frac{1}θ)}(\M)\odot E_2^{(\frac{1}{1-θ})}(\M)\;(0<θ<1). $$ As application, we extend these result to the noncommutative symmetric quasi Hardy spaces case. We also obtained the real case of Peter Jones' theorem for noncommutative symmetric quasi Hardy spaces.

math.OA↗
arXiv2015

Noncommutative martingale inequalities associated with convex functions

We report recent advances on noncommutative martingale inequalities associated with convex functions. These include noncommutative Burkholder-Gundy inequalities associated with convex functions due to the present authors and Dirksen and Ricard, noncommutative maximal inequalities associated with convex functions due to Osȩkowski and the present authors, and noncommutative Burkholder and Junge-Xu inequalities associated with convex functions due to Randrianantoanina and Lian Wu. Some open problems for noncommutative martingales are also included.

math.OA↗
arXiv2014

Noncommutative maximal inequalities associated with convex functions

We prove several noncommutative maximal inequalities associated with convex functions, including a Doob type inequality for a convex function of maximal operators on noncommutative martingales, noncommutative Dunford-Schwartz and Stein maximal ergodic inequalities for a convex function of positive and symmetric positive contractions. The key ingredient in our proofs is a Marcinkiewicz type interpolation theorem for a convex function of maximal operators in the noncommutative setting, which we establish in this paper. These generalize the results of Junge and Xu in the $L^p$ case to the case of convex functions.

math.OA↗
arXiv2010

Noncommutative weak Orlicz spaces and martingale inequalities

This paper is devoted to the study of noncommutative weak Orlicz spaces and martingale inequalities. Marcinkiewicz interpolation theorem is extended to include noncommutative weak Orlicz spaces as interpolation classes. In particular, we prove the weak type $Φ$-moment Burkholder-Gundy inequality for noncommutative martingales through establishing a weak type $Φ$-moment noncommutative Khintchine's inequality for Rademacher's random variables.

math.FA↗
arXiv2010

Interpolation and $Φ$-moment inequalities of noncommutative martingales

This paper is devoted to the study of $Φ$-moment inequalities for noncommutative martingales. In particular, we prove the noncommutative $Φ$-moment analogues of martingale transformations, Stein's inequalities, Khintchine's inequalities for Rademacher's random variables, and Burkholder-Gundy's inequalities. The key ingredient is a noncommutative version of Marcinkiewicz type interpolation theorem for Orlicz spaces which we establish in this paper.

math.OA↗
arXiv2007

Riesz and Szegö type factorizations for noncommutative Hardy spaces

Let $\A$ be a finite subdiagonal algebra in Arveson's sense. Let $H^p(\A)$ be the associated noncommutative Hardy spaces, $0<p\le\8$. We extend to the case of all positive indices most recent results about these spaces, which include notably the Riesz, Szegö and inner-outer type factorizations. One new tool of the paper is the contractivity of the underlying conditional expectation on $H^p(\A)$ for $p<1$.

math.OA↗