Piotr Budzynski

On unbounded composition operators in L^2-spaces

Fundamental properties of unbounded composition operators in

Unbounded weighted composition operators in l²-spaces

L^2

Dense definiteness and boundedness of composition operators in L^2-spaces via inductive limits

-spaces are studied. Characterizations of normal and quasinormal composition operators are provided. Formally normal composition operators are shown to be normal. Composition operators generating Stieltjes moment sequences are completely characterized. The unbounded counterparts of the celebrated Lambert’s characterizations of subnormality of bounded composition operators are shown to be false. Various illustrative examples are supplied.

Unbounded composition operators via inductive limits: Cosubnormal operators with matrix symbols, II

It is shown that for every positive integer n there exists a subnormal weighted shift on a directed tree (with or without root) whose nth power is densely defined while its ()th power is not. As a consequence, for every positive integer n there exists a nonsymmetric subnormal composition operator C in an L2-space over a σ-finite measure space such that Cn is densely defined and is not.

Unbounded composition operators via inductive limits: cosubnormals with matrical symbols

Bounded and unbounded weighted composition operators on

Subnormality: General Criteria

L^2

Relationships Between C ϕ , w and C ϕ

spaces over

Discrete Measure Spaces

\sigma