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COMMON LOCAL SPECTRAL PROPERTIES OF INTERTWINING LINEAR OPERATORS

Yoo, Jong-Kwang;Han, Hyuk

  • Received : 2009.03.30
  • Accepted : 2009.05.19
  • Published : 2009.06.25

Abstract

Let T ${\in}$ $\mathcal{L}$(X), S ${\in}$ $\mathcal{L}$(Y ), A ${\in}$ $\mathcal{L}$(X, Y ) and B ${\in}$ $\mathcal{L}$(Y,X) such that SA = AT, TB = BS, AB = S and BA = T. Then S and T shares that same local spectral properties SVEP, property (${\beta}$), property $({\beta})_{\epsilon}$, property (${\delta}$) and decomposability. From these common local spectral properties, we give some results related with Aluthge transforms and subscalar operators.

Keywords

Local Spectral Theory;Bishop's Property ${\beta}$;Decomposable Operators;Subscalar Operators

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