6533b7d6fe1ef96bd1266b4b
RESEARCH PRODUCT
A decomposition of Denjoy-Khintchine-Pettis and Henstock-Kurzweil-Pettis integrable multifunctions
Luisa Di PiazzaK. Musialsubject
Settore MAT/05 - Analisi MatematicaMultifunctions Pettis set-valued integral Kurzweil-Henstock integral Kurzweil-Henstock-Pettis integral support function Denjoy-Khintchine-Pettis integral selectors.description
We proved in one of our earlier papers that in case of separable Banach space valued multifunctions each Henstock-Kurzweil-Pettis integrable multifunction can be represented as a sum of one of its Henstock-Kurzweil-Pettis integrable selector and a Pettis integrable multifunction. Now, we prove that the same result can be achieved in case of an arbitrary Banach space. Moreover we show that an analogous result holds true also for the Denjoy-Khintchine-Pettis integrable multifunctions. Applying the representation theorem we describe the multipliers of HKP and DKP integrable functions. Then we use this description to obtain an operator characterization of HKP and DKP integrability.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2010-01-01 |