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• W1489475456 abstract "For a bounded linear operator $Tin L(X)$ on a complex Banach space $X$ and a closed subset $F$ of the complex plane $mathbb {C},$ this note deals with algebraic representations of the corresponding analytic spectral subspace $X_{T}(F)$ from local spectral theory. If $T$ is the restriction of a generalized scalar operator to a closed invariant subspace, then it is shown that $X_{T}(F)=E_{T}(F)=bigcap _{hspace {0.03cm}lambda notin F}left ( lambda -Tright ) ^{hspace {0.03cm}p}X$ for all sufficiently large integers $p,$ where $E_{T}(F)$ denotes the largest linear subspace $Y$ of $X$ for which $left ( lambda -Tright ) Y=Y$ for all $lambda in mathbb {C} setminus F.$ Moreover, for a wide class of operators $T$ that satisfy growth conditions of polynomial or Beurling type, it is shown that $X_{T}(F)$ is closed and equal to $E_{T}(F).$" @default.
• W1489475456 created "2016-06-24" @default.
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• W1489475456 date "2003-10-03" @default.
• W1489475456 modified "2023-10-07" @default.
• W1489475456 title "Spectral subspaces of subscalar and related operators" @default.
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• W1489475456 doi "https://doi.org/10.1090/s0002-9939-03-07217-4" @default.
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