论文标题
无限制的M-刺激性操作员的非对称fuglede-putnam定理
Asymmetric Fuglede-Putnam Theorem for Unbounded M-Hyponormal Operators
论文作者
论文摘要
Hilbert Space $ \ Mathcal {H} $在Hilbert Space上的密集定义的$ T $如果$ \ Mathcal {d}（t）\ subset \ subset \ mathcal {d}（t^{^}）$，则$ m> par pallall par parlalter（ m \ Parallel（t-Zi）x \ Parallel $ for All $ z \ in \ Mathbb {C} $，以及\ Mathcal {d}（t）$的所有$ x \ in \ yathbb {c} $。在本文中，我们证明，如果有限的线性运算符$ a：\ Mathcal {h} \ rightarrow \ Mathcal \ Mathcal {k} $，以至于$ ab^*\ subseteq ta $，其中$ b $是封闭的subormortor（resp。A$ m $ -hyponormal noble $ h $ -hyponormal），上面$ \ natercalcalcal in $ \ $ \ $ \ $ $ $ $ { $ \ MATHCAL {H} $上的封闭的子正常），然后（i）$ ab \ subseteq t^*a，$（ii）$ {\ overline {ran（a^{*}}} $将$ b $降低到普通运营商$ b \ vert _ { （iii）$ {\ overline {ran（a）}} $将$ t $减少到普通运算符$ t \ vert _ {\ overline {ran（a）}}} $。
A closed densely defined operator $ T $ on a Hilbert space $ \mathcal{H} $ is callled $M$-hyponormal if $\mathcal{D}(T) \subset \mathcal{D}(T^{*}) $ and there exists $ M > 0 $ for which $ \parallel(T-zI)^{*}x \parallel \leq M \parallel(T-zI)x \parallel $ for all $ z \in \mathbb{C}$ and for all $ x\in \mathcal{D}(T)$. In this paper, we prove that if bounded linear operator $ A : \mathcal{H} \rightarrow \mathcal{K}$ is such that $ AB^*\subseteq TA $, where $ B $ is a closed subnormal (resp. a closed $ M $-hyponormal) on $\mathcal{H}$, $ T $ is a closed $ M $-hyponormal (resp. a closed subnormal) on $\mathcal{H}$, then (i) $ AB\subseteq T^*A, $ (ii) $ {\overline{ran(A^{*})}} $ reduces $ B $ to the normal operator $ B\vert_{{\overline{ran(A^{*})}}}, $ and (iii) $ {\overline{ran(A)}} $ reduces $ T $ to the normal operator $ T\vert_{\overline{ran(A)}}.$
