Generalized spectrum and commuting compact perturbations
1993 ◽
Vol 36
(2)
◽
pp. 197-209
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Keyword(s):
Let X be an infinite-dimensional complex Banach space and denote the set of bounded (compact) linear operators on X by B(X) (K(X)). Let N(A) and R(A) denote, respectively, the null space and the range space of an element A of B(X). Set R(A∞)=∩nR(An) and k(A)=dim N(A)/(N(A)∩R(A∞)). Let σg(A) = ℂ\{λ∈ℂ:R(A−λ) is closed and k(A−λ)=0} denote the generalized (regular) spectrum of A. In this paper we study the subset σgb(A) of σg(A) defined by σgb(A) = ℂ\{λ∈ℂ:R(A−λ) is closed and k(A−λ)<∞}. Among other things, we prove that if f is a function analytic in a neighborhood of σ(A), then σgb(f(A)) = f(σgb(A)).
1986 ◽
Vol 28
(2)
◽
pp. 193-198
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2020 ◽
Vol 39
(6)
◽
pp. 1435-1456
1990 ◽
Vol 32
(3)
◽
pp. 273-276
◽
2019 ◽
Vol 38
(3)
◽
pp. 133-140
Keyword(s):
1969 ◽
Vol 21
◽
pp. 592-594
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