اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدGeneralized Browders and Weyls theorems for left and right multiplication operators
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The main objective of this work is to study generalized Browders and Weyls theorems for the multiplication operators $L_A$ and $R_B$ and for the elementary operator $tau_{A,B}=L_AR_B$.
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Given Banach spaces $X$ and $Y$ and operators $Ain B(X)$ and $Bin B(Y)$, property $(gw)$ does not in general transfer from $A$ and $B$ to the tensor product operator $Aotimes Bin B(Xoverline{otimes} Y)$ or to the elementary operator defined by $A$ an
d $B$, $tau_{AB}=L_AR_Bin B(B(Y,X))$. In this article necessary and sufficient conditions ensuring that property $(gw)$ transfers from $A$ and $B$ to $Aotimes B$ and to $tau_{AB}$ will be given.
The transfer property for the generalized Browders theorem both of the tensor product and of the left-right multiplication operator will be characterized in terms of the $B$-Weyl spectrum inclusion. In addition, the isolated points of these two classes of operators will be fully characterized.
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A Banach space operator $Tin B(X)$ is left polaroid if for each $lambdainhbox{iso}sigma_a(T)$ there is an integer $d(lambda)$ such that asc $(T-lambda)=d(lambda)<infty$ and $(T-lambda)^{d(lambda)+1}X$ is closed; $T$ is finitely left polaroid if asc $
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