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http://dx.doi.org/10.14317/jami.2011.29.1_2.459

BISHOP'S PROPERTY (${\beta}$) AND SPECTRAL INCLUSIONS ON BANACH SPACES  

Yoo, Jong-Kwang (Department of Liberal Arts and Science, Chodang University)
Oh, Heung-Joon (Department of Liberal Arts and Science, Chodang University)
Publication Information
Journal of applied mathematics & informatics / v.29, no.1_2, 2011 , pp. 459-468 More about this Journal
Abstract
Let T ${\in}$ L(X), S ${\in}$ L(Y), A ${\in}$ L(X, Y) and B ${\in}$ L(Y, X) such that SA = AT, TB = BS, AB = S and BA = T. Then S and T shares the same local spectral properties SVEP, Bishop's property (${\beta}$), property $({\beta})_{\epsilon}$, property (${\delta}$) and and subscalarity. Moreover, the operators ${\lambda}I$ - T and ${\lambda}I$ - S have many basic operator properties in common.
Keywords
Bishop's Property (${\beta}$); decomposable operators; local spectral theory; subscalar operators;
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