Tensor Products and Singularly Continuous Spectrum
Canadian mathematical bulletin, Tome 27 (1984) no. 4, pp. 481-484

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

An example of a bounded self adjoint operator A is constructed so that A⊗I + α(I⊗A) is purely singularly continuous but A⊗1 + β(I⊗A) is purely absolutely continuous, for some real α and β. In fact α - β can be chosen arbitrarily small.
DOI : 10.4153/CMB-1984-076-6
Mots-clés : 47A10
White, Denis A. W. Tensor Products and Singularly Continuous Spectrum. Canadian mathematical bulletin, Tome 27 (1984) no. 4, pp. 481-484. doi: 10.4153/CMB-1984-076-6
@article{10_4153_CMB_1984_076_6,
     author = {White, Denis A. W.},
     title = {Tensor {Products} and {Singularly} {Continuous} {Spectrum}},
     journal = {Canadian mathematical bulletin},
     pages = {481--484},
     year = {1984},
     volume = {27},
     number = {4},
     doi = {10.4153/CMB-1984-076-6},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1984-076-6/}
}
TY  - JOUR
AU  - White, Denis A. W.
TI  - Tensor Products and Singularly Continuous Spectrum
JO  - Canadian mathematical bulletin
PY  - 1984
SP  - 481
EP  - 484
VL  - 27
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1984-076-6/
DO  - 10.4153/CMB-1984-076-6
ID  - 10_4153_CMB_1984_076_6
ER  - 
%0 Journal Article
%A White, Denis A. W.
%T Tensor Products and Singularly Continuous Spectrum
%J Canadian mathematical bulletin
%D 1984
%P 481-484
%V 27
%N 4
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1984-076-6/
%R 10.4153/CMB-1984-076-6
%F 10_4153_CMB_1984_076_6

[1] 1. Berberian, S. K., Produit de Convolution des Mesures Operatorielles, Acta Sci. Math., 40 (1978), 3-8. Google Scholar

[2] 2. Colgen, R. and Klockner, K., Absolutely Continuous Tensor Products and Applications to Scattering Theory Bull. Acad. Polon. Sci. Ser. Sci. Math 28 (1980), 37-40. Google Scholar

[3] 3. Ichinose, T., Spectral Properties of Tensor Products of Linear Operators I, Trans. Am. Math. Soc. 235(1978), 75-113. Google Scholar | DOI

[4] 4. Ichinose, T., Spectral Properties of Tensor Products of Linear Operators, Trans. Am. Math. Soc. 237(1978), 223-254. Google Scholar

[5] 5. Jessen, B. and Wintner, A., Distribution Functions and the Riemann Zeta Functions Trans. Am. Math. Soc. 38 (1935), 48-89. Google Scholar | DOI

[6] 6. Mourre, E., Absence of Singular Spectrum for Certain Self-Adjoint Operators, Commun. Math. Phys. 78 (1981, 391-408). Google Scholar | DOI

[7] 7. Perry, P., Sigal, I. M., and Simon, B., Spectral Analysis of N-Body Schrödinger Operators, Ann. Math. 114(1981), 519-567. Google Scholar | DOI

[8] 8. Progovečki, E.. Quantum Mechanics in Hilbert Space, Academic Press, New York, 1971. Google Scholar

[9] 9. Reed, M. and Simon, B., Methods of Modern Mathematical Physics, Vol. I, Academic Press, New York, 1972. Google Scholar

Cité par Sources :