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Let X, Y   be Banach spaces, A:X→YA:XY and B,C:Y→XB,C:YX be bounded linear operators satisfying operator equation ABA=ACAABA=ACA. In this paper, we show that AC and BA share the local spectral properties such as Bishop's property (β), subscalarity and Dunford's property (C). Also, the quasi-nilpotent part and the analytic core for AC and BA are studied.  相似文献
2.
A three-space theorem for upper semi-Fredholmness (resp. lower semi-Fredholmness) is proved.  相似文献
3.
Motivated by a paper of Fang (2009), we study the Samuel multiplicity and the structure of essentially semi-regular operators on an infinite-dimensional complex Banach space. First, we generalize Fang’s results concerning Samuel multiplicity from semi-Fredholm operators to essentially semi-regular operators by elementary methods in operator theory. Second, we study the structure of essentially semi-regular operators. More precisely, we present a revised version of Fang’s 4 × 4 upper triangular model with a little modification, and prove it in detail after providing numerous preliminary results, some of which are inspired by Fang’s paper. At last, as some applications, we get the structure of semi-Fredholm operators which revised Fang’s 4 × 4 upper triangular model, from a different viewpoint, and characterize a semi-regular point λ ∈ ? in an essentially semi-regular domain.  相似文献
4.
It is shown that local spectral properties such as the single-valued extension property, Dunford’s property(C), Bishop’s property(β), the decomposition property(δ), or decomposability are stable under commuting perturbations whose spectra are finite.  相似文献
5.
Let X, Y be Banach spaces, and B, be bounded linear operators satisfying the operator equation . Recently, as extensions of Jacobson's lemma, Corach, Duggal and Harte studied common properties of and in algebraic viewpoint and also obtained some topological analogues. In this note, we continue to investigate common properties of AC and BA from the viewpoint of spectral theory. In particular, we give an affirmative answer to one question posed by Corach et al. by proving that has closed range if and only if has closed range.  相似文献
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