Geodesic
Local spectrum and local spectral radius of an operator at a fixed vector
Janko Bračič 1   ; Vladimír Müller 2
1 IMFM, University of Ljubljana Jadranska ul. 19 SI-1000 Ljubljana, Slovenia
2 Mathematical Institute Czech Academy of Sciences Žitná 25 115 67 Praha 1, Czech Republic
Studia Mathematica, Tome 194 (2009) no. 2, pp. 155-162 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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Let $\mathscr X$ be a complex Banach space and $e\in\mathscr X$ a nonzero vector. Then the set of all operators $T\in{\cal L}(\mathscr X)$ with $\sigma_T(e)=\sigma_\delta(T)$, respectively $r_T(e)=r(T)$, is residual. This is an analogy to the well known result for a fixed operator and variable vector. The results are then used to characterize linear mappings preserving the local spectrum (or local spectral radius) at a fixed vector $e$.
DOI : 10.4064/sm194-2-3
Keywords: mathscr complex banach space mathscr nonzero vector set operators cal mathscr sigma sigma delta respectively residual analogy known result fixed operator variable vector results characterize linear mappings preserving local spectrum local spectral radius fixed vector nbsp

Janko Bračič  1   ; Vladimír Müller  2

1 IMFM, University of Ljubljana Jadranska ul. 19 SI-1000 Ljubljana, Slovenia
2 Mathematical Institute Czech Academy of Sciences Žitná 25 115 67 Praha 1, Czech Republic 
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Janko Bračič; Vladimír Müller. Local spectrum and local spectral radius
 of an operator at a fixed vector. Studia Mathematica, Tome 194 (2009) no. 2, pp. 155-162. doi: 10.4064/sm194-2-3

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