First, some classic properties of a weighted Frobenius-Perron operator on as a predual of weighted Koopman operator on will be investigated using the language of the conditional expectation operator. Also, we determine the spectrum of under certain conditions.
We describe the centered weighted composition operators on 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 , the set of all bounded normal operators on a Hilbert space and then some topological properties of are investigated.
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