Geodesic
On Decomposability of Compact Perturbations of Normal Operators
Canadian journal of mathematics, Tome 27 (1975) no. 3, pp. 725-735

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

The main purpose of this paper is to show that a bounded Hilbert-space operator whose imaginary part is in the Schatten class Cp(1 ≦ p < ∞ ) is strongly decomposable. This answers affirmatively a question raised by Colojoara and Foias [6, Section 5(e), p. 218].In case 0 ≦ T* — T ∈ C1, it was shown by B. Sz.-Nagy and C. Foias [2, p. 442; 25, p. 337] that T has many properties analogous to those of a decomposable operator and by A. Jafarian [11] that T is strongly decomposable. The authors of [11] and [24] employ the properties of the characteristic function of the contraction operator obtained from the Cayley transform of T; 
Radjabalipour, M.; Radjavi, H. On Decomposability of Compact Perturbations of Normal Operators. Canadian journal of mathematics, Tome 27 (1975) no. 3, pp. 725-735. doi: 10.4153/CJM-1975-080-8
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