On extended commuting operators


Sungeun Jung, Hyoungji Kim, Eungil Ko




In this paper, we study properties of extended commuting operators. In particular, we provide the polar decomposition of the product of (λ, µ)-commuting operators where λ and µ are real numbers with λµ > 0. Furthermore, we find the restriction of µ for the product of (λ, µ)-commuting quasihyponormal operators to be quasihyponormal. We also give spectral and local spectral relations between λ-commuting operators. Moreover, we show that the operators λ-commuting with a unilateral shift are representable as weighted composition operators