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.
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2010 Mathematics Subject Classification. Primary 47A10, 47A11, 47B20 Keywords. λ-commuting operators, (λ, µ)-commuting operators, polar decomposition, quasihyponormal operators Received: 09 March 2020; Accepted: 03 April 2021 Communicated by Dragan S. Djordjević This work was supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIT) (2019R1F1A1058633) and the Ministry of Education (2019R1A6A1A11051177). The first author was supported by Hankuk University of Foreign Studies Research Fund and was supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIT) (2017R1C1B1008965). Email addresses: firstname.lastname@example.org (Sungeun Jung), email@example.com (Hyoungji Kim), firstname.lastname@example.org (Eungil Ko)
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- (λ,µ)-commuting operators
- Polar decomposition
- Quasihyponormal operators
- λ-commuting operators