6th Summer Workshop on Operator Theory

9th - 13th July 2018 Kraków

Piotr Budzyński

Weighted composition operators in L2-spaces

Given a σ-finite measure space (X,A,μ), an A-measurable transformation φ of X, and a complex A-measurable function w on X, the weighted composition operator in L2(μ) induced by φ and w is given by

D(Cf,w) = {f ∈ L2(μ): w⋅(f∘φ) ∈ L2(μ)},

Cf,w f = w⋅(f∘φ), f ∈ D(Cf,w),

The talk is aimed at presenting a variety of results concerning normality, seminormality, selfadjointness, and subnormality of bounded and unbounded weighted composition operators acting in φ-spaces.

The talk is based on joint work with Zenon Jałoński, Il Bong Jung, and Jan Stochel.

  1. P. Budzyński, Z. J. Jabłoński, I. B. Jung, J. Stochel, Unbounded weighted composition operators in L2-spaces, Lecture Notes in Math. 2209 (2018).
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