Continuous sums of measures and continuous spectra
Glasgow mathematical journal, Tome 7 (1965) no. 1, pp. 9-14
Voir la notice de l'article provenant de la source Cambridge University Press
Von Neumann's definition of the continuous sum of Hilbert spaces led Segal [3] to define the continuous sum of measures on a measurable space. In this note we employ Segal's definition to investigate the measure structures associated with a self-adjoint transformation of pure point spectrum and a self-adjoint transformation of pure continuous spectrum. While these transformations, as operators on separable Hilbert spaces, are the antithesis of each other we show that in their measure structure one is a particular case of the other.
Sankaran, S. Continuous sums of measures and continuous spectra. Glasgow mathematical journal, Tome 7 (1965) no. 1, pp. 9-14. doi: 10.1017/S2040618500035073
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author = {Sankaran, S.},
title = {Continuous sums of measures and continuous spectra},
journal = {Glasgow mathematical journal},
pages = {9--14},
year = {1965},
volume = {7},
number = {1},
doi = {10.1017/S2040618500035073},
url = {http://geodesic.mathdoc.fr/articles/10.1017/S2040618500035073/}
}
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