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Differences of Stević–Sharma operators
Banach Journal of Mathematical Analysis ( IF 1.2 ) Pub Date : 2020-01-24 , DOI: 10.1007/s43037-019-00051-z
Shuming Wang , Maofa Wang , Xin Guo

A generalization of the products of composition, multiplication and differentiation operators is the Stevic–Sharma operator $$T_{u_1,u_2,\varphi }$$ , defined by $$T_{u_1,u_2,\varphi }f=u_1\cdot f\circ \varphi +u_2\cdot f'\circ \varphi $$ , where $$u_1,u_2,\varphi $$ are holomorphic functions on the unit disk $${\mathbb {D}}$$ in the complex plane $${\mathbb {C}}$$ and $$\varphi ({\mathbb {D}})\subset {\mathbb {D}}$$ . We are interested in the difference of Stevic–Sharma operators which has never been considered so far. In this paper, we characterize its boundedness, compactness and order boundedness between Banach spaces of holomorphic functions. As an important special case, we obtain the above characterizations of the difference of weighted composition operators. Furthermore, we show the equivalence of order boundedness and Hilbert-Schmidtness for the difference of composition operators between Hardy or weighted Bergman spaces.

中文翻译:

Stević–Sharma 算子的差异

合成、乘法和微分算子的乘积的概括是 Stevic–Sharma 算子 $$T_{u_1,u_2,\varphi }$$ ,定义为 $$T_{u_1,u_2,\varphi }f=u_1\cdot f\circ \varphi +u_2\cdot f'\circ \varphi $$ ,其中 $$u_1,u_2,\varphi $$ 是复形单元盘 $${\mathbb {D}}$$ 上的全纯函数平面 $${\mathbb {C}}$$ 和 $$\varphi ({\mathbb {D}})\subset {\mathbb {D}}$$ 。我们对迄今为止从未考虑过的 Stevic-Sharma 算子的差异感兴趣。在本文中,我们刻画了全纯函数的 Banach 空间之间的有界性、紧致性和阶有界性。作为一个重要的特例,我们得到了上述加权组合算子差异的表征。此外,
更新日期:2020-01-24
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