Papers by Turdebek Bekjan
Dominated convergence theorems in Haagerup noncommutative $$L_p$$-spaces
Advances in Operator Theory
A Beurling–Blecher–Labuschagne type theorem for Haagerup noncommutative $$L^p$$ spaces
Banach Journal of Mathematical Analysis
Interpolation and the John–Nirenberg inequality on symmetric spaces of noncommutative martingales
Studia Mathematica
Annals of Functional Analysis, Nov 16, 2021
We introduce noncommutative weak Orlicz spaces associated with a weight and study their propertie... more 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.
HAL (Le Centre pour la Communication Scientifique Directe), May 14, 2007
Let A be a finite subdiagonal algebra in Arveson's sense. Let H p (A) be the associated noncommut... more Let A be a finite subdiagonal algebra in Arveson's sense. Let H p (A) be the associated noncommutative Hardy spaces, 0 < p ≤ ∞. 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.
arXiv: Operator Algebras, 2019
Let $\mathcal{M}$ be a $\sigma$-finite von Neumann algebra, equipped with a normal faithful state... more Let $\mathcal{M}$ be a $\sigma$-finite von Neumann algebra, equipped with a normal faithful state $\varphi$, and let $\mathcal{A}$ be maximal subdiagonal subalgebra of $\mathcal{M}$. We prove a Beurling-Blecher-Labuschagne theorem for $\mathcal{A}$-invariant subspaces of $L^p(\mathcal{M})$ when $1\le p<\infty$. As application, we give a characterization of outer operators in Haagerup noncommutative $H^{p}$-spaces associated with $\mathcal{A}$.
Annals of Functional Analysis, 2021
We introduce noncommutative weak Orlicz spaces associated with a weight and study their propertie... more 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.
Acta Mathematica Scientia, 2019
We proved a complex interpolation theorem of noncommutative Hardy spaces associated with semi-fin... more We proved a complex interpolation theorem of noncommutative Hardy spaces associated with semi-finite von Neumann algebras and extend the Riesz type factorization to the semi-finite case.
Mathematische Zeitschrift, 2017
We show the dual spaces of conditional Hardy space and symmetric Hardy space of noncommutative ma... more We show the dual spaces of conditional Hardy space and symmetric Hardy space of noncommutative martingales. We derive relationship between the symmetric Hardy space of noncommutative martingales and its conditioned version.
Szegö type factorization of Haagerup noncommutative Hardy spaces
Acta Mathematica Scientia, 2017
Abstract Let M be a σ-finite von Neumann algebra equipped with a normal faithful state φ, and let... more Abstract Let M be a σ-finite von Neumann algebra equipped with a normal faithful state φ, and let A be a maximal subdiagonal algebra of M . We proved a Szego type factorization theorem for the Haagerup noncommutative H p -spaces.
On interpolation of noncommutative symmetric Hardy spaces
Positivity, 2017
We proved the noncommutative analogue of Calderón’s result for fully symmetric spaces $$E_1$$E1 a... more We proved the noncommutative analogue of Calderón’s result for fully symmetric spaces $$E_1$$E1 and $$E_2$$E2 on (0, 1) and for a finite von Neumann algebra $${{\mathcal {M}}}$$M. We also proved the noncommutative symmetric Hardy space’s analogue of Calderón’s result for fully symmetric spaces and for finite subdiagonal subalgebras.
Interpolation of noncommutative symmetric martingale spaces
Journal of Operator Theory, 2017
Transactions of the American Mathematical Society, 2016
We prove several noncommutative maximal inequalities associated with convex functions, including ... more 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, and 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.
Some advances on theory of noncommutative H p spaces
Noncommutative Hardy space associated with semi-finite subdiagonal algebras
Journal of Mathematical Analysis and Applications, 2015
ABSTRACT
The noncommutative $$H^{(r,s)}_{p}({\mathcal A};\ell _{\infty })$$ H p ( r , s ) ( A ; ℓ ∞ ) and $$H_{p}({\mathcal A};\ell _{1})$$ H p ( A ; ℓ 1 ) spaces
Positivity, 2015
In this paper we introduce the noncommutative $$H^{(r,s)}_{p}({\mathcal A};\ell _{\infty })$$Hp(r... more In this paper we introduce the noncommutative $$H^{(r,s)}_{p}({\mathcal A};\ell _{\infty })$$Hp(r,s)(A;ℓ∞) and $$H_{p}({\mathcal A};\ell _{1})$$Hp(A;ℓ1) spaces, and prove the contractivity of the underlying conditional expectation $$\varPhi $$Φ on these spaces. We also give results on duality and complex interpolation.
Noncommutative Symmetric Hardy Spaces
Integral Equations and Operator Theory, 2014
ABSTRACT
Toeplitz operators associated with semifinite von neumann algebra
Acta Mathematica Scientia, 2015
ABSTRACT
In this paper, we establish a Marcinkiewicz type interpolation theorem for convex functions of ma... more In this paper, we establish a Marcinkiewicz type interpolation theorem for convex functions of maximal functions in the noncommutative setting. As applications, we prove the noncommutative analogue of the Doob inequality for convex functions of maximal functions on martingales, the analogue of the classical Dunford-Schwartz maximal ergodic inequality for convex functions of positive contractions, and that of Stein's maximal inequality for convex functions of symmetric positive contractions. As a consequence, we obtain the moment Burkholder-Davis-Gundy inequality for noncommutative martingales.
$\Phi-Inequalities of Noncommutative Martingales
Rocky Mountain Journal of Mathematics, 2006
ABSTRACT In the recent article [Commun. Math. Phys. 189, No. 3, 667–698 (1997; Zbl 0898.46056)] G... more ABSTRACT In the recent article [Commun. Math. Phys. 189, No. 3, 667–698 (1997; Zbl 0898.46056)] G. Pisier and Q. Xu showed that, among other things, the noncommutative analogue of the classical Burkholder-Gandy inequalities in martingale theory. We prove the noncommutative analogue of the classical Φ-inequalities for commutative martingale.
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Papers by Turdebek Bekjan