Abstract
Let T <TEX>${\in}$</TEX> <TEX>$\mathcal{L}$</TEX>(X), S <TEX>${\in}$</TEX> <TEX>$\mathcal{L}$</TEX>(Y ), A <TEX>${\in}$</TEX> <TEX>$\mathcal{L}$</TEX>(X, Y ) and B <TEX>${\in}$</TEX> <TEX>$\mathcal{L}$</TEX>(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 (<TEX>${\beta}$</TEX>), property <TEX>$({\beta})_{\epsilon}$</TEX>, property (<TEX>${\delta}$</TEX>) and decomposability. From these common local spectral properties, we give some results related with Aluthge transforms and subscalar operators.
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