Ann. Funct. Anal. 6 (2015), no. 1, 109–115 http://doi.org/10.15352/afa/06-1-9 ISSN: 2008-8752 (electronic) http://projecteuclid.org/afa p-QUASIPOSINORMAL COMPOSITION AND WEIGHTED COMPOSITION OPERATORS ON L 2 (μ) ANURADHA GUPTA 1 AND NEHA BHATIA 2* Communicated by Y. Lim Abstract. An operator T on a Hilbert space H is called p-quasiposinormal operator if c 2 T * (T * T ) p T ≥ T * (TT * ) p T where 0 <p ≤ 1 and for some c> 0. In this paper, we have obtained conditions for composition and weighted composition operators to be p-quasiposinormal operators. Introduction and preliminaries Let H be an infinite dimensional complex Hilbert space and B(H ) be the algebra of all bounded operators on H . An operator T is called p-quasiposinormal [6] if for some c> 0 and 0 <p ≤ 1, it satisfies the inequality c 2 T * (T * T ) p T ≥ T * (TT * ) p T. Let T be a measurable transformation on X. The composition operator C T on the space L 2 (μ) is given by C T f = f ◦ T for f ∈ L 2 (μ) Let φ be a complex-valued measurable function then the weighted composition operator W φ,T on the space L 2 (μ) induced by φ and T is given by W φ,T f = φ · f ◦ T for f ∈ L 2 (μ) In [1], G.Datt has described the conditions for the composition and weighted composition operators to be k-quasiposinormal operators. The aim of this paper is to study the p-quasiposinormal composition and p-quasiposinormal weighted com- position operators and their corresponding adjoints in terms of Radon–Nikodym Date : Received: May 6, 2013; Accepted: Jul. 29, 2013. * Corresponding author. 2010 Mathematics Subject Classification. Primary 47B38; Secondary 47B20, 47B33. Key words and phrases. composition operators, conditional expectation operators, p- quasiposinormal operators, weighted composition operators. 109