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• W2629192011 abstract "We characterize the properties $(z)$ and $(az)$ for an operator $T$ whose dual $T^*$ has the SVEP on the complementary of the upper semi-Weyl spectrum of $T.$ If $S$ and $T$ are Banach space operators satisfying property $(z)$ or $(az),$ we give conditions on $S$ and $T$ to ensure the preservation of these properties by the direct sum $Soplus T.$ Some results are given for multipliers and in general for $(H)$-operators. Also we give a correct proof of cite[Theorem 2.3]{SZ} which was proved by using the equality $sigma_p^0(Soplus T)= sigma_p^0(S)cup sigma_p^0(T).$ However this equality is not true; we give counterexamples to show that." @default.
• W2629192011 created "2017-06-30" @default.
• W2629192011 creator A5012093112 @default.
• W2629192011 creator A5085758141 @default.
• W2629192011 date "2017-06-24" @default.
• W2629192011 modified "2023-09-27" @default.
• W2629192011 title "Property (z); direct sums and a note on an a-Browder type theorem" @default.
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