On composition operators. (English) Zbl 0815.47040
This paper is devoted to the study of composition operators on \(\sigma\)- finite standard Borel spaces. The first paragraph generalizes some ancient results concerning the characterization of Fredholm composition operators. The following two sections are dedicated to composition operators with ascent 1 and descent 1; a criterion for establishing partial isometry and co-isometry of operators is given. The last paragraph is concerned with hyponormal composition operators on square summable weighted standard Borel spaces.
Reviewer: I.Gottlieb (Iaşi)
MSC:
47B38 | Linear operators on function spaces (general) |
47B20 | Subnormal operators, hyponormal operators, etc. |
47A53 | (Semi-) Fredholm operators; index theories |