In this paper, we study the relation between local spectral properties of the linear operators RS and SR. We show that RS and SR share the same local spectral properties SVEP, (β), (δ) and decomposability. We also show that RS is subscalar if and only if SR is subscalar. We recapture some known results on spectral properties of Aluthge transforms.
Abstract. A multicontraction on a Hilbert space H is an n-tuple of operators T = (T 1 , . . . , Tn) acting on H, such thatWe obtain some results related to the characteristic function of a commuting multicontraction, most notably discussing its behaviour with respect to the action of the analytic automorphisms of the unit ball.
Abstract. Let R and S be commuting n-tuples. We give some spectral and local spectral relations between RS and SR. In particular, we show that RS has the single valued extension property or satisfies Bishop's property (β) if and only if SR has the corresponding property.
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