Multiplication Operators on the Bloch Space of Bounded Homogeneous Domains

نویسنده

  • ROBERT F. ALLEN
چکیده

In this paper, we study the multiplication operators on the Bloch space of a bounded homogeneous domain in C. Specifically, we characterize the bounded and the compact multiplication operators, establish estimates on the operator norm, and determine the spectrum. Furthermore, we prove that for a large class of bounded symmetric domains, the isometric multiplication operators are those whose symbol is a constant of modulus one.

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 from H∞ to the Bloch Space of a Bounded Homogeneous Domain

Let D be a bounded homogeneous domain in C. In this paper, we study the bounded and the compact weighted composition operators mapping the Hardy space H∞(D) into the Bloch space of D. We characterize the bounded weighted composition operators, provide operator norm estimates, and give sufficient conditions for compactness. We prove that these conditions are necessary in the case of the unit bal...

متن کامل

Essential norm estimates of generalized weighted composition operators into weighted type spaces

Weighted composition operators appear in the study of dynamical systems and also in characterizing isometries of some classes of Banach spaces. One of the most important generalizations of weighted composition operators, are generalized weighted composition operators which in special cases of their inducing functions give different types of well-known operators like: weighted composition operat...

متن کامل

A Class of compact operators on homogeneous spaces

Let  $varpi$ be a representation of the homogeneous space $G/H$, where $G$ be a locally compact group and  $H$ be a compact subgroup of $G$. For  an admissible wavelet $zeta$ for $varpi$  and $psi in L^p(G/H), 1leq p <infty$, we determine a class of bounded  compact operators  which are related to continuous wavelet transforms on homogeneous spaces and they are called localization operators.

متن کامل

Localization operators on homogeneous spaces

Let $G$ be a locally compact group, $H$ be a compact subgroup of $G$ and $varpi$ be a representation of the homogeneous space $G/H$ on a Hilbert space $mathcal H$. For $psi in L^p(G/H), 1leq p leqinfty$, and an admissible wavelet $zeta$ for $varpi$, we define the localization operator $L_{psi,zeta} $ on $mathcal H$ and we show that it is a bounded operator. Moreover, we prove that the localizat...

متن کامل

Norm of the multiplication operators from H∞ to the Bloch Space of a bounded symmetric domain

Let D be a bounded symmetric domain in C and let ψ be a complex-valued holomorphic function on D. In this work, we determine the operator norm of the bounded multiplication operator with symbol ψ from the space of bounded holomorphic functions on D to the Bloch space of D when ψ fixes the origin. If no restriction is imposed on the symbol ψ, we have a formula for the operator norm when D is the...

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 2009