论文标题
在$ g_ {z} $ - kato的分解和概括Koliha drazin的概括
On the $g_{z}$-Kato decomposition and generalization of Koliha Drazin invertibility
论文作者
论文摘要
在\ cite {koliha}中，koliha证明了$ t \ in L（x）$（$ x $是一个复杂的Banach Space）是普遍化的Drazin Drazin可逆操作员，等同于存在$ s $ s $的$ t $，与$ t $交通，$ t $ sts = s $ sts = s $ and $ c $ s yes eq.（ $ 0 \ in \ mbox {acc} \，σ（t）。$后来，在\ cite {rwassa，rwassa，rwassa1}中扩展了一类通用的drazin可逆操作员，它们还扩展了MBEKHTA \ cite} pseudo-fredholm operators classe claste and pseeudo-fredo-fredholm operator半粉红色运营商。 As a continuation of these works, we introduce and study the class of $g_{z}$-invertible (resp., $g_{z}$-Kato) operators which generalizes the class of generalized Drazin invertible operators (resp., the class of generalized Kato-meromorphic operators introduced by Živković-Zlatanović and Duggal in \ cite {rwassa2}）。除其他结果外，我们证明$ t $是$ g_ {z} $ - 仅当$ t $是$ g_ {z {z} $ - 带有$ \ tilde {p}（t）= \ tilde {q}（q}（q}（t）（t）（t）<\ infty $等于$ $ $ $ $ t $ t的$ tilde = $ \ mbox {acc} \，σ（t^{2} s- t）\ subset \ {0 \} $又等同于说$ 0 \ not \ in \ mbox {acc} \ in \ mbox {acc} \，（\ mbox {ac c} Browder-type定理的特征。
In \cite{koliha}, Koliha proved that $T\in L(X)$ ($X$ is a complex Banach space) is generalized Drazin invertible operator equivalent to there exists an operator $S$ commuting with $T$ such that $STS = S$ and $σ(T^{2}S - T)\subset\{0\}$ which is equivalent to say that $0\not\in \mbox{acc}\,σ(T).$ Later, in \cite{rwassa,rwassa1} the authors extended the class of generalized Drazin invertible operators and they also extended the class of pseudo-Fredholm operators introduced by Mbekhta \cite{mbekhta} and other classes of semi-Fredholm operators. As a continuation of these works, we introduce and study the class of $g_{z}$-invertible (resp., $g_{z}$-Kato) operators which generalizes the class of generalized Drazin invertible operators (resp., the class of generalized Kato-meromorphic operators introduced by Živković-Zlatanović and Duggal in \cite{rwassa2}). Among other results, we prove that $T$ is $g_{z}$-invertible if and only if $T$ is $g_{z}$-Kato with $\tilde{p}(T)=\tilde{q}(T)<\infty$ which is equivalent to there exists an operator $S$ commuting with $T$ such that $STS = S$ and $\mbox{acc}\,σ(T^{2}S - T)\subset\{0\}$ which in turn is equivalent to say that $0\not\in \mbox{acc}\,(\mbox{acc}\,σ(T)).$ As application and using the concept of the Weak SVEP introduced at the end of this paper, we give new characterizations of Browder-type theorems.
