Schatten class Toeplitz operators acting on large weighted Bergman spaces
نویسندگان
چکیده
منابع مشابه
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.
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Namita Das P. G. Department of Mathematics, Utkal University, Vanivihar, Bhubaneswar, Orissa 751004, India Correspondence should be addressed to Namita Das, [email protected] Received 23 July 2009; Revised 7 September 2009; Accepted 14 October 2009 Recommended by Palle Jorgensen We have shown that if the Toeplitz operator Tφ on the Bergman space La D belongs to the Schatten class Sp, 1 ≤...
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In this note we consider the hyponormality of Toeplitz operators Tφ on the Weighted Bergman space Aα(D) with symbol in the class of functions f + g with polynomials f and g of degree 2. Mathematics subject classification (2010): 47B20, 47B35.
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For α > −1, let A2α be the corresponding weighted Bergman space of the unit ball in C. For a bounded measurable function f , let Tf be the Toeplitz operator with symbol f on A 2 α. This paper describes all the functions f for which Tf commutes with a given Tg, where g(z) = z1 1 · · · z Ln n for strictly positive integers L1, . . . , Ln, or g(z) = |z1| s1 · · · |zn| nh(|z|) for non-negative real...
متن کاملOperators on weighted Bergman spaces
Let ρ : (0, 1] → R+ be a weight function and let X be a complex Banach space. We denote by A1,ρ(D) the space of analytic functions in the disc D such that ∫ D |f(z)|ρ(1 − |z|)dA(z) < ∞ and by Blochρ(X) the space of analytic functions in the disc D with values in X such that sup|z|<1 1−|z| ρ(1−|z|)‖F ′(z)‖ < ∞. We prove that, under certain assumptions on the weight, the space of bounded operator...
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ژورنال
عنوان ژورنال: Studia Mathematica
سال: 2015
ISSN: 0039-3223,1730-6337
DOI: 10.4064/sm8345-12-2015