Geodesic
ON VECTOR-VALUED SPECTRA
Glasgow mathematical journal, Tome 42 (2000) no. 2, pp. 247-253

Voir la notice de l'article provenant de la source Cambridge University Press

Elements\alpha\in A\otimes E of the tensor product of a Banach algebra Aand a Banach space E induce systems \{\psi(\alpha):\psi\in E^*\}of elements of A indexed by the dual space E^*, whose jointspectrum belongs to the second dual E^{**}. In this note we investigate when thespectrum actually lies in E\subseteq E^{**}, and extend the spectral mappingtheorem P\sigma_A(\alpha)=\sigma_AP(\alpha) to polynomial mappings P:E\toF between Banach spaces. When the algebra A is commutative and the Banachspace E=B is another algebra we also reach a sort of vector-valued Gelfandtheory. 
HARTE, ROBIN; TAYLOR, CIARAN. ON VECTOR-VALUED SPECTRA. Glasgow mathematical journal, Tome 42 (2000) no. 2, pp. 247-253. doi: 10.1017/S0017089500020103
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     title = {ON {VECTOR-VALUED} {SPECTRA}},
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     year = {2000},
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     doi = {10.1017/S0017089500020103},
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