Geodesic
Invertible Operators on Certain Banach Spaces
Canadian mathematical bulletin, Tome 20 (1977) no. 2, pp. 153-160

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It has long been the practice in the theory of Hilbert spaces to use the Fourier series expansion (i.e. the Levy inversion formula) for the resolution of the identity associated with a unitary operator to obtain results for this operator, and hence for any power bounded invertible operator on such spaces since they are necessarily isomorphic to unitary operators [5, p. 1945]. Though many important power bounded operators on Banach spaces are not spectral [6, p. 1045-1051] the approach of this paper permits us to deduce for such operators results similar to those known for spectral operators. 
Belley, J.-M. Invertible Operators on Certain Banach Spaces. Canadian mathematical bulletin, Tome 20 (1977) no. 2, pp. 153-160. doi: 10.4153/CMB-1977-027-3
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     title = {Invertible {Operators} on {Certain} {Banach} {Spaces}},
     journal = {Canadian mathematical bulletin},
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     year = {1977},
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     number = {2},
     doi = {10.4153/CMB-1977-027-3},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1977-027-3/}
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