摘要
Let н be a complex, separable, infinite dimensional Hilbert space, T ε(H). (u+K)(T) denotes the (u+k)-orbit of T, i.e., (u+k)(T) = {R-1TR: R is invertible and of the form unitary plus compact}. Let be an analytic and simply connected Cauchy domain in C and n ε N. A(, n) denotes the class of operators, each of which satisfies (i) T is essentially normal; (ii) σ(T) =, ρF(T) ∩ σ(T) = ; (iii) ind (λ-T) = -n, nul (λ-T) = 0 (λ∈Ω ). It is proved that given T1, T2 ε A(, n) and ε > 0, there exists a compact operator K with K <ε such that T1 +Kε (u+k)(T2). This result generalizes a result of P. S. Guinand and L. Marcoux [6,15]. Furthermore, the authors give a character of the norm closure of (u+K)(T), and prove that for each T ε A(, n), there exists a compact (SI) perturbation of T whose norm can be arbitrarily small.