论文标题
电源有限界操作员在Banach空间上的衍生界限功能演算
Derivative bounded functional calculus of power bounded operators on Banach spaces
论文作者
论文摘要
在本文中，我们在Banach Space上研究有限的操作员$ t $ $ X $，该$ x $满足离散的Gomilko shi-feng条件$$ \ int_ {0}^{2π} | \ langle r（re^{it}，t），t）^{2} \ frac {c} {（r^2-1）} \ norme {x} \ norme {x^*}，\ quad r> 1，x \ in x，x^*\ in x^*。 $$我们表明，它等效于某个衍生界有界的功能演算，也相对于BESOV空间相对于有界的功能演算。同样在Hilbert空间上，离散的Gomilko shi-feng条件也等同于束缚。最后，我们讨论了涉及$γ$结合的概念的Banach空间的最后一个等同。
In this article we study bounded operators $T$ on Banach space $X$ which satisfy the discrete Gomilko Shi-Feng condition $$\int_{0}^{2π}|\langle R(re^{it},T)^{2}x,x^*\rangle |dt \leq \frac{C}{(r^2-1)}\norme{x}\norme{x^*},\quad r>1, x\in X, x^* \in X^*. $$ We show that it is equivalent to a certain derivative bounded functional calculus and also to a bounded functional calculus relative to Besov space. Also on Hilbert space discrete Gomilko Shi-Feng condition is equivalent to power-boundedness. Finally we discuss the last equivalence on general Banach space involving the concept of $γ$-boundedness.
