6533b7d4fe1ef96bd12628b5
RESEARCH PRODUCT
On compactness of the difference of composition operators
Pekka NieminenEero Saksmansubject
Pure mathematicsConjectureComposition operatorApplied Mathematics010102 general mathematicsMathematical analysiseducationdifferenceComposition (combinatorics)Space (mathematics)01 natural sciences010101 applied mathematicsCompact spaceUnit circlecomposition operator111 Mathematicscompactness0101 mathematicsUnit (ring theory)Aleksandrov measureAnalysisMathematicsdescription
Abstract Let φ and ψ be analytic self-maps of the unit disc, and denote by C φ and C ψ the induced composition operators. The compactness and weak compactness of the difference T = C φ − C ψ are studied on H p spaces of the unit disc and L p spaces of the unit circle. It is shown that the compactness of T on H p is independent of p ∈[1,∞). The compactness of T on L 1 and M (the space of complex measures) is characterized, and examples of φ and ψ are constructed such that T is compact on H 1 but non-compact on L 1 . Other given results deal with L ∞ , weakly compact counterparts of the previous results, and a conjecture of J.E. Shapiro.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2004-10-01 |