caa a22 4500 605462356 CHVBK 20210128100247.0 cr unu---uuuuu 210128e20151101xx s 000 0 eng 10.1007/s10114-015-5116-5 doi (NATIONALLICENCE)springer-10.1007/s10114-015-5116-5 Common properties of the operator products in local spectral theory [Elektronische Daten] [Kai Yan, Xiao Fang] Let X, Y be Banach spaces, A,D: X → Y and B,C: Y → X be the bounded linear operators satisfying operator equation set $\left\{ \begin{gathered} ACD = DBD, \hfill \\ DBA = ACA. \hfill \\ \end{gathered} \right. $ . In this paper, we show that AC and BD share some basic operator properties such as the injectivity and the invertibility. Moreover, we show that AC and BD share many common local spectral properties including SVEP, Bishop property (β) and Dunford property (C). Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag Berlin Heidelberg, 2015 Jacobson's lemma nationallicence operator equation set nationallicence common property nationallicence local spectral theory nationallicence Yan Kai Department of Mathematics, Tongji University, 200092, Shanghai, P. R. China aut Fang Xiao Department of Mathematics, Tongji University, 200092, Shanghai, P. R. China aut Acta Mathematica Sinica, English Series Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society 31/11(2015-11-01), 1715-1724 1439-8516 31:11<1715 2015 31 10114 https://doi.org/10.1007/s10114-015-5116-5 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10114-015-5116-5 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Yan Kai Department of Mathematics, Tongji University, 200092, Shanghai, P. R. China aut NATIONALLICENCE 700 1- Fang Xiao Department of Mathematics, Tongji University, 200092, Shanghai, P. R. China aut NATIONALLICENCE 773 0- Acta Mathematica Sinica, English Series Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society 31/11(2015-11-01), 1715-1724 1439-8516 31:11<1715 2015 31 10114