Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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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)
  • Received : 2010.07.09
  • Accepted : 2010.08.20
  • Published : 2011.01.30
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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.

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References

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