论文标题
$ l $ - 道具中心和狭窄的操作员
$L$-orthogonality in Daugavet centers and narrow operators
论文作者
论文摘要
我们研究了$ L $ - 正交元素与Daugavet中心和狭窄的运营商有关。我们证明，如果$ \ dens（y）\ leqω_1$和$ g：x \ longrightArrow y $是一个道路中心，则$ g（w）$包含一些$ l $ -Orthodal，对于每个非空的$ w^*$ - $ w^*$ - $ b_ {x^{**} $ b_ {x^{**} $的$ w^*$ - 在狭窄的运营商的背景下，我们表明，如果$ x $是可分离的，而$ t：x \ longrightArrow y $是狭窄的运营商，然后在b_x $中给出$ y \ y \ y \ y in b_x $和任何非空的$ w^*$ - 开放式$ w $ of $ b_ of $ b_ {x^{**} $，那么$ w $ and $ w $ lun $ l $ l $ - $ t^{**}（u）= t（y）$。在$ t^*（y^*）$可分开的特殊情况下，我们将先前的结果扩展到$ \ dens（x）=ω_1$。最后，我们证明，以前的结果都不具有更大的密度字符（特别是在Continuum假设下以$ω_2$显示了反例）。
We study the presence of $L$-orthogonal elements in connection with Daugavet centers and narrow operators. We prove that, if $\dens(Y)\leq ω_1$ and $G:X\longrightarrow Y$ is a Daugavet center, then $G(W)$ contains some $L$-orthogonal for every non-empty $w^*$-open subset of $B_{X^{**}}$. In the context of narrow operators, we show that if $X$ is separable and $T:X\longrightarrow Y$ is a narrow operator, then given $y\in B_X$ and any non-empty $w^*$-open subset $W$ of $B_{X^{**}}$ then $W$ contains some $L$-orthogonal $u$ so that $T^{**}(u)=T(y)$. In the particular case that $T^*(Y^*)$ is separable, we extend the previous result to $\dens(X)=ω_1$. Finally, we prove that none of the previous results holds in larger density characters (in particular, a counterexample is shown for $ω_2$ under continuum hypothesis).
