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- Title
The (U + K)-Orbit of Essentially Normal Operators and Compact Perturbations of Strongly Irreducible Operators.
- Authors
Ji, Youqing; Jiang, Chunlan; Wang, Zongyao
- Abstract
Let H be a complex, separable, infinite dimensional Hilbert space, T ∈ L(H). (U + K)(T) denotes the (U + K)-orbit of T, i.e., (U + K)(T) = {R[sup -1]TR: R is invertible and of the form unitary plus compact}. Let Ω be an analytic and simply connected Cauchy domain in C and n ∈ N. A(Ω, n) denotes the class of operators, each of which satisfies (i) T is essentially normal; (ii) [formula]; (iii) ind(λ - T) = -n, nul(λ - T) = 0 (λ ∈ Ω). It is proved that given T[sub 1], T[sub 2] ∈ A(Ω, n) and ε > 0, there exists a compact operator K with ||K|| < ε such that T[sub 1] + K ∈ (U + K)(T[sub 2]). This result generalizes a result of P. S. Guinand and L. Marcoux[sup [6, 15]]. Furthermore, the authors give a character of the norm closure of (U + K)(T), and prove that for each T ∈ A(Ω, n), there exists a compact (SI) perturbation of T whose norm can be arbitrarily small. [formula available in full text].
- Subjects
PERTURBATION theory; IRREDUCIBLE polynomials; ORBIT method
- Publication
Chinese Annals of Mathematics, 2000, Vol 21, Issue 2, p237
- ISSN
0252-9599
- Publication type
Article
- DOI
10.1142/S0252959900000273