论文标题
drazin可逆$（m，p）$ - 膨胀运营商
Drazin invertible $(m,P)$-expansive operators
论文作者
论文摘要
Hilbert太空运营商$ t \ in B $是$（m，p）$ - 膨胀，对于某些正整数$ m $和b $中的运营商$ p \，如果$ \ sum_ {j = 0}^m {（ - 1）^j \ left（\ begin {array} {clcr} m \\ j \ end {array} \ right）没有drazin可逆运算符$ t $可以是$（m，i）$ - 膨胀，如果$ t $是$（m，p）$ - 对于某些正运算符$ p $的扩张，则一定是$ p $的分解$ p = p = p_ {11}}} \ oplus 0 $。如果$ t $是$（m，| t^n |^2）$ - 用于某些正整数$ n $的扩展，则$ t^n $具有分解$ t^n = \ left（\ begin {array} {clcr} u_1p_1p_1＆x＆x＆x＆x＆x \ \ x \ \ 0＆0＆0＆0＆end aray {array} {aray} \ right right）$;如果还$ \ left（\ begin {array} {clcr} i_1＆x \\ x^*＆x^*＆x^* x \ end end {array} \ right）\ geq i $ $，然后$ \ left（\ begin {arnay} $（m，i）$ - 扩展和$ \ left（\ begin {array} {clcr} p^{\ frac {\ frac {1} {2}} _1u_1p^{\ frac {1} {1} {1} {2} {2}} {2}} _1＆p_1＆p_1＆p_1^{\ frac { 0 \ end {array} \ right）$ is $（m，i）$ - 在$ h $上等效规范中扩展。
A Hilbert space operator $T\in B$ is $(m,P)$-expansive, for some positive integer $m$ and operator $P\in B$, if $\sum_{j=0}^m{(-1)^j\left(\begin{array}{clcr}m\\j\end{array}\right)T^{*j}PT^j}\leq 0$. No Drazin invertible operator $T$ can be $(m,I)$-expansive, and if $T$ is $(m,P)$-expansive for some positive operator $P$, then necessarily $P$ has a decomposition $P=P_{11}\oplus 0$. If $T$ is $(m,|T^n|^2)$-expansive for some positive integer $n$, then $T^n$ has a decomposition $T^n=\left(\begin{array}{clcr}U_1P_1 & X\\0 & 0\end{array}\right)$; if also $\left(\begin{array}{clcr}I_1 & X\\X^* & X^*X\end{array}\right)\geq I$, then $\left(\begin{array}{clcr}P_1U_1 & P_1X\\0 & 0\end{array}\right)$ is $(m,I)$-expansive and $\left(\begin{array}{clcr}P^{\frac{1}{2}}_1U_1P^{\frac{1}{2}}_1 & P_1^{\frac{1}{2}}X\\0 & 0\end{array}\right)$ is $(m,I)$-expansive in an equivalent norm on $H$.
