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Let T 2 L(X), S 2 L(Y ); A 2 L(X;Y ) and B 2 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 (fl), property (fl)†, property (-) and decomposability. From these common local spectral properties, we give some results related with Aluthge transforms and subscalar operators.

COMMON LOCAL SPECTRAL PROPERTIES OF INTERTWINING LINEAR OPERATORS