Turdebek N. Bekjan

The dual of noncommutative Lorentz spaces

We prove some noncommutative analogues of the classical results about dual spaces of the classical Lorentz spaces.

Noncommutative orlicz-hardy spaces

Abstract Let (Φ, Ψ) be a pair of complementary N-functions and H Φ ( A ) and H Ψ ( A ) be the associated noncommutative Orlicz-Hardy spaces. We extend the Riesz, Szego and inner-outer type factorization theorems of H p ( A ) to this case.

Characterization of subdiagonal algebras

Let M be a finite von Neumann algebra with a faithful normal tracial state T , and let A be a tracial subalgebra of M. We show that A has L P -factorization (1 ≤ p < oo) if and only if A is a subdiagonal algebra. Also, we obtain some characterizations of subdiagonal algebras.

Φ-INEQUALITIES AND LAWS OF LARGE NUMBERS OF HARDY MARTINGALE TRANSFORMS

Abstract Using stopping time method we proved the Φ-inequalities, pointwise convergence, strong and weak laws of large numbers of Hardy martingale transforms with values in complex Banach spaces, and applying them to give several characterizations of AUMD spaces.

ON Lp-MATRICIALLY NORMED SPACES

Abstract It is proved that there is only one Lp-matricially normed space of dimension 1 and that quotient spaces of Lp-matricially normed spaces are also Lp-matricially normed spaces. Some properties of Lp-matricially normed spaces are given.

Some properties of semifinite tracial subalgebras

Abstract We obtained some characterizations of Jensen type inequalities in tracial subalgebras and gave some characterizations of subdiagonal algebras of semifinite von Neumann algebras.

SZEGO TYPE FACTORIZATION OF HAAGERUP NONCOMMUTATIVE HARDY SPACES

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.

TOEPLITZ OPERATORS ASSOCIATED WITH SEMIFINITE VON NEUMANN ALGEBRA

Abstract Let H2(M) be a noncommutative Hardy space associated with semifinite von Neumann algebra M, we get the connection between numerical spectrum and the spectrum of Toeplitz operator Tt acting on H2(M), and the norm of Toeplitz operator Tt is equivalent to ||t|| when t is hyponormal operator in M.