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

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

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
@article{10_4153_CMB_1977_027_3,
     author = {Belley, J.-M.},
     title = {Invertible {Operators} on {Certain} {Banach} {Spaces}},
     journal = {Canadian mathematical bulletin},
     pages = {153--160},
     year = {1977},
     volume = {20},
     number = {2},
     doi = {10.4153/CMB-1977-027-3},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1977-027-3/}
}
TY  - JOUR
AU  - Belley, J.-M.
TI  - Invertible Operators on Certain Banach Spaces
JO  - Canadian mathematical bulletin
PY  - 1977
SP  - 153
EP  - 160
VL  - 20
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1977-027-3/
DO  - 10.4153/CMB-1977-027-3
ID  - 10_4153_CMB_1977_027_3
ER  - 
%0 Journal Article
%A Belley, J.-M.
%T Invertible Operators on Certain Banach Spaces
%J Canadian mathematical bulletin
%D 1977
%P 153-160
%V 20
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1977-027-3/
%R 10.4153/CMB-1977-027-3
%F 10_4153_CMB_1977_027_3

[1] 1. Belley, J.-M., Invertible Measure Preserving Transformations and Pointwise Convergence, Proc. Amer. Math. Soc., Vol. 43, No. 1, March 1974, p. 159-162. Google Scholar

[2] 2. Belley, J.-M., Spectral Properties for Invertible Measure Preserving Transformations, Can. J. Math., Vol. XXV, No. 4, 1973, p. 808-811. Google Scholar

[3] 3. Colojoară, I. and Foiaş, C., Theory of Generalized Spectral Operators, Gordon and Beach, Science Publishers, New York, 1968. Google Scholar

[4] 4. Davis, H., Fourier Series and Orthogonal Functions, Allyn and Bacon, Boston, Mass., 1963. Google Scholar

[5] 5. Dunford, N. and Schwartz, J. T., Linear Operators, Part HI, Wiley-Interscience, New York, 1971. Google Scholar

[6] 6. Fixman, U., Problems in Spectral Operators, Pacific J. Math. 9 (1959), p. 1029-1051. Google Scholar

[7] 7. Foiaş, C., Sur les mesures qui interviennent dans la théorie ergodique, J. Math. Mech., 13, No. 4, 1964, p. 639-658. Google Scholar

[8] 8. Halmos, P. R., Lectures on Ergodic Theory, Publ. Math. Soc. Japan, No. 3, The Mathematical Society of Japan, Tokyo, 1956. Google Scholar

[9] 9. Riesz, F. and Sz.-Nagy, B., Lecons d'analyse fonctionnelle, Akadémiai Kiadó, Budapest, 1952, sixth edition. Google Scholar

[10] 10. Royden, H. L., Real Analysis, Macmillan Company, New York, 1968. Google Scholar

[11] 11. Sz.-Nagy, B., On uniformly bounded linear transformations in Hilbert space, Acta. Sci. Math. (Szeged) 11 (1947), p. 152-157. Google Scholar

[12] 12. Sz.-Nagy, B. and Foiaş, C., Harmonic Analysis of Operators on Hilbert Space, Akadémiai Kiado, Budapest, 1970. Google Scholar

Cité par Sources :