The space of spectral measures is a homogeneous reductive space |
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| Authors: | E. Andruchow L. Recht D. Stojanoff |
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| Affiliation: | (1) Instituto Argentino de Matemática, Viamonte 1636, 1055 Buenos Aires, Argentina;(2) Departamento de Matemática, Universidad Simón Bolívar, Apartado Postal 89000, Caracas, Venezuela |
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| Abstract: | We prove that the space of spectral measures on a W*-algebra is a smooth Banach manifold in a natural way and that the action of the group of invertible elements of the algebra by inner automorphisms makes it into a reductive homogeneous space. This gives a geometric structure for the set of normal operators with the same spectrum. |
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| Keywords: | 47B15 58B10 |
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