Annals of Functional Analysis

Common properties of the operator products in spectral theory

Xiaochun Fang and Kai Yan

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Let $X, Y$ be Banach spaces, $A, D: X\rightarrow Y$ and $B, C: Y\rightarrow X$ be the bounded linear operators satisfying operator equation set $$\left\{ \begin{aligned} ACD=DBD~ \\ DBA=ACA. \\ \end{aligned} \right.. $$ The concept of regularity was firstly introduced by Kordula and M$\ddot{u}$ller. In this paper, we investigate the common properties of $AC$ and $BD$ in viewpoint of regularity when $A, B, C$ and $D$ all satisfy the operator equation set above.

Article information

Ann. Funct. Anal., Volume 6, Number 4 (2015), 60-69.

First available in Project Euclid: 1 July 2015

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 47A10: Spectrum, resolvent
Secondary: 47A53: (Semi-) Fredholm operators; index theories [See also 58B15, 58J20] 47A55: Perturbation theory [See also 47H14, 58J37, 70H09, 81Q15]

Jacobson's lemma operator equation set common property regularity


Yan, Kai; Fang, Xiaochun. Common properties of the operator products in spectral theory. Ann. Funct. Anal. 6 (2015), no. 4, 60--69. doi:10.15352/afa/06-4-60.

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