论文标题
弱星准标准获得运营商
Weak-star quasi norm attaining operators
论文作者
论文摘要
For Banach spaces $X$ and $Y$, a bounded linear operator $T\colon X \longrightarrow Y^*$ is said to weak-star quasi attain its norm if the $σ(Y^*,Y)$-closure of the image by $T$ of the unit ball of $X$ intersects the sphere of radius $\|T\|$ centred at the origin in $Y^*$.这个概念的灵感来自于在\ cite {ccjm}中引入和研究的运算符的准标准达到的启发。作为主要结果，我们证明，在有限的线性运算符的空间中，无论Banach空间的选择如何，弱星形标准范围实现运算符的集合是密集的，此外，近似运算符也可以与其他属性一起选择。这使我们能够区分弱星准标准实现运算符的属性与实现运算符的准官能运营商的属性。还表明，在某些条件下，弱星准标准达到运营商与其他类型的规范属性运营商共享等效属性的数量，但是在许多情况下，它们与其他情况的行为不同。
For Banach spaces $X$ and $Y$, a bounded linear operator $T\colon X \longrightarrow Y^*$ is said to weak-star quasi attain its norm if the $σ(Y^*,Y)$-closure of the image by $T$ of the unit ball of $X$ intersects the sphere of radius $\|T\|$ centred at the origin in $Y^*$. This notion is inspired by the quasi-norm attainment of operators introduced and studied in \cite{CCJM}. As a main result, we prove that the set of weak-star quasi norm attaining operators is dense in the space of bounded linear operators regardless of the choice of the Banach spaces, furthermore, that the approximating operator can be chosen with additional properties. This allows us to distinguish the properties of weak-star quasi norm attaining operators from those of quasi norm attaining operators. It is also shown that, under certain conditions, weak-star quasi norm attaining operators share numbers of equivalent properties with other types of norm attaining operators, but that there are also a number of situations in which they behave differently from the others.
