Dense definiteness and boundedness of composition operators in   $L^2$-spaces via inductive limits
  The questions of dense definiteness and boundedness of composition operators in $L^2$-spaces are studied by means of inductive limits of operators. Methods based on projective systems of measure spaces and inductive limits of $L^2$-spaces are developed. Illustrative examples are presented. 
Piotr Budzynski, Artur Planeta
math.FA