论文标题
涉及无限运营商$ p（t）$，$ tt^*$和$ t^*t $的某些属性；以及对无限运营商的权力和$ nth $根的应用
Certain properties involving the unbounded operators $p(T)$, $TT^*$, and $T^*T$; and some applications to powers and $nth$ roots of unbounded operators
论文作者
论文摘要
在本文中，我们关注的是$ [p（t）]^*= \ bar {p}（t^*）$的条件，其中$ p（z）$是一种单变量的复杂多项式，而$ t $是无限制的，密集的定义和线性操作员。然后，我们处理身份的有效性$σ（ab）=σ（ba）$，其中$ a $ a $ a $ a $ b $是两个无界运营商。等式$（tt^*）^*= tt^*$和$（t^*t）^*= t^*t $，其中$ t $是一个密集定义的可闭合操作员。特定的利息将支付给等式$ t^*t = p（t）$及其变体。然后，我们有一些有关$ nth $ nth $ roots类的正常和非正态（无限）运算符的结果。我们的结果伴随着一些进一步的后果和反例。
In this paper, we are concerned with conditions under which $[p(T)]^*=\bar{p}(T^*)$, where $p(z)$ is a one-variable complex polynomial, and $T$ is an unbounded, densely defined, and linear operator. Then, we deal with the validity of the identities $σ(AB)=σ(BA)$, where $A$ and $B$ are two unbounded operators. The equations $(TT^*)^*=TT^*$ and $(T^*T)^*=T^*T$, where $T$ is a densely defined closable operator, are also studied. A particular interest will be paid to the equation $T^*T=p(T)$ and its variants. Then, we have certain results concerning $nth$ roots of classes of normal and nonnormal (unbounded) operators. Some further consequences and counterexamples accompany our results.
