We describe the centered weighted composition operators on L 2 (Σ) in terms of their defining symbols. Our characterizations extend Embry-Wardrop-Lambert’s theorem on centered composition operators.
Some stronger and equivalent metrics are defined on M, the set of all bounded normal operators on a Hilbert space H and then some topological properties of M are investigated.
First, some classic properties of a weighted Frobenius-Perron operator P u ϕ on L 1 (Σ) as a predual of weighted Koopman operator W = uUϕ on L∞(Σ) will be investigated using the language of the conditional expectation operator. Also, we determine the spectrum of P u ϕ under certain conditions