New results and open problems on Toeplitz operators in Bergman spaces

نویسندگان

  • A. Perälä
  • J. Taskinen
  • J. A. Virtanen
  • J. A. VIRTANEN
چکیده

We discuss some of the recent progress in the field of Toeplitz operators acting on Bergman spaces of the unit disk, formulate some new results, and describe a list of open problems—concerning boundedness, compactness and Fredholm properties—which was presented at the conference “Recent Advances in Function Related Operator Theory” in Puerto Rico in March 2010.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Weighted composition operators on weighted Bergman spaces and weighted Bloch spaces

In this paper, we characterize the bonudedness and compactness of weighted composition operators from weighted Bergman spaces to weighted Bloch spaces. Also, we investigate weighted composition operators on weighted Bergman spaces and extend the obtained results in the unit ball of $mathbb{C}^n$.

متن کامل

Toeplitz and Hankel Operators on a Vector-valued Bergman Space

In this paper, we derive certain algebraic properties of Toeplitz and Hankel operators defined on the vector-valued Bergman spaces L2,C n a (D), where D is the open unit disk in C and n ≥ 1. We show that the set of all Toeplitz operators TΦ,Φ ∈ LMn(D) is strongly dense in the set of all bounded linear operators L(L2,Cn a (D)) and characterize all finite rank little Hankel operators.

متن کامل

ar X iv : 0 90 3 . 06 51 v 3 [ m at h . C V ] 1 8 A ug 2 00 9 Toeplitz operators on generalized Bergman spaces

We consider the weighted Bergman spaces HL(B, μλ), where we set dμλ(z) = cλ(1−|z| 2) dτ (z), with τ being the hyperbolic volume measure. These spaces are nonzero if and only if λ > d. For 0 < λ ≤ d, spaces with the same formula for the reproducing kernel can be defined using a Sobolev-type norm. We define Toeplitz operators on these generalized Bergman spaces and investigate their properties. S...

متن کامل

Schatten class Toeplitz operators on weighted Bergman spaces of the unit ball

For positive Toeplitz operators on Bergman spaces of the unit ball, we determine exactly when membership in the Schatten classes Sp can be characterized in terms of the Berezin transform.

متن کامل

Finite Rank Toeplitz Operators in Bergman Spaces

We discuss resent developments in the problem of description of finite rank Toeplitz operators in different Bergman spaces and give some applications

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2010