Asymptotic and Partial Asymptotic Hankel Operators on H2(Dn)).

In this paper, we generalize the concept of asymptotic Hankel operators on H 2 (D) to the Hardy space H 2 (D n) (over polydisk) in terms of asymptotic Hankel and partial asymptotic Hankel operators and investigate some properties in case of its weak and strong convergence. Meanwhile, we introduce ith-partial Hankel operators on H 2 (D n) and obtain a characterization of its compactness for n > 1. Our main results include the containment of Toeplitz algebra in the collection of all strong partial asymptotic Hankel operators on H 2 (D n) . It is also shown that a Toeplitz operator with symbol ϕ is asymptotic Hankel if and only if ϕ is holomorphic function in L ∞ (T n) . [ABSTRACT FROM AUTHOR]