On Decomposability of Compact Perturbations of Normal Operators
1975 ◽
Vol 27
(3)
◽
pp. 725-735
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Keyword(s):
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;
Keyword(s):
1963 ◽
Vol 59
(4)
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pp. 727-729
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1965 ◽
Vol 17
◽
pp. 1030-1040
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Keyword(s):
2017 ◽
Vol 11
(01)
◽
pp. 1850004
Keyword(s):
2007 ◽
pp. 255-302