Abstract
Let H denote a complex, separable, infinite-dimensional Hilbert space, and denote by CSA(n,H) the set of commuting n-tuples of selfadjoint operators on H. A normed ideal (J, ∣ ∣j) of operators on H will be called a diagonalization ideal if for every t in CSA(n,H) there is a diagonalizable t′ in CSA(n,H) such that t-t′ ∈ Jn (where the exponent indicates the Cartesian product of n copies of J), An ideal which is not a diagonalization ideal will be called an obstruction ideal. We shall only consider symmetrically normed ideals (or s.n. ideals); cf. [1].
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References
I.T. Gohberg and M.G. Krein, Introduction to the theory of non-selfadjoint operators, Nauka, Moscow, 1965.
T. Kato, Perturbation theorey for linear operators, Springer, New York, 1966.
D. Voiculescu, Some results on norm-ideal perturbations of Hilbert space operators, J. Operator Theory 2(1979), 3–37.
D. Voiculescu, On the existence of quasicentral approximate units relative to normed ideals. I, preprint.
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Dedicated to Professor Israel Gohberg on the occasion of his sixtieth birthday.
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© 1989 Birkhäuser Verlag Basel
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Bercovici, H., Voiculescu, D. (1989). The Analogue of Kuroda’s Theorem for n-Tuples. In: Dym, H., Goldberg, S., Kaashoek, M.A., Lancaster, P. (eds) The Gohberg Anniversary Collection. Operator Theory: Advances and Applications, vol 41. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-9278-0_5
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DOI: https://doi.org/10.1007/978-3-0348-9278-0_5
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-0348-9975-8
Online ISBN: 978-3-0348-9278-0
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