Essential commutants on strongly pseudo-convex domains
نویسندگان
چکیده
Consider a bounded strongly pseudo-convex domain Ω with smooth boundary in Cn. Let T be the Toeplitz algebra on Bergman space La2(Ω). That is, is C⁎-algebra generated by operators {Tf:f∈L∞(Ω)}. Extending work [27], [28] special case of unit ball, we show that any such Ω, and {Tf:f∈VObdd}+K are essential commutants each other, where K collection compact On general considered this paper, proofs require many new ideas techniques. These same techniques also enable us to for A∈T, if 〈Akz,kz〉→0 as z→∂Ω, then A operator.
منابع مشابه
On the quadratic support of strongly convex functions
In this paper, we first introduce the notion of $c$-affine functions for $c> 0$. Then we deal with some properties of strongly convex functions in real inner product spaces by using a quadratic support function at each point which is $c$-affine. Moreover, a Hyers–-Ulam stability result for strongly convex functions is shown.
متن کاملThe Pluricomplex Poisson Kernel for Strongly Convex Domains
In the past decades the study of pluri-potential theory and of its applications played a central role in complex analysis in several variables. In particular, since the basic work of Siciak [31] and Bedford and Taylor [7], [8] a great effort was made to understand the complex MongeAmpère operator and the associated generalized Dirichlet problems (for instance, see [15], [20] and references ther...
متن کاملON STRONGLY h-CONVEX FUNCTIONS
We introduce the notion of strongly h-convex functions (defined on a normed space) and present some properties and representations of such functions. We obtain a characterization of inner product spaces involving the notion of strongly h-convex functions. Finally, a Hermite–Hadamard–type inequality for strongly h-convex functions is given.
متن کاملEstimates for the ∂̄−neumann Operator on Strongly Pseudo-convex Domain with Lipschitz Boundary
On a bounded strongly pseudo-convex domain X in C with a Lipschitz boundary, we prove that the ∂̄−Neumann operator N can be extended as a bounded operator from Sobolev (−1/2)−spaces to the Sobolev (1/2)−spaces. In particular, N is compact operator on Sobolev (−1/2)−spaces.
متن کاملPrescribing Zeros of Functions in the Nevanlinna Class on Weakly Pseudo-convex Domains in C2
Let D be a bounded weakly pseudo-convex domain in C2 of uniform strict type. For any positive divisor M of D with finite area, there exists a holomorphic function / in the Nevanlinna class such that M is the zero set of /. The proof is to study the solutions of 8 with Ll(dD) boundary values. 2 Let D be a bounded weakly pseudo-convex domain in C .In this paper we study the Poincaré-Lelong equati...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Functional Analysis
سال: 2021
ISSN: ['0022-1236', '1096-0783']
DOI: https://doi.org/10.1016/j.jfa.2020.108775