A decomposition of Denjoy-Khintchine-Pettis and Henstock-Kurzweil-Pettis integrable multifunctions

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Abstract

We proved in one of our earlierpapers that in case of separable Banach space valuedmultifunctions each Henstock-Kurzweil-Pettis integrablemultifunction can be represented as a sum of one of itsHenstock-Kurzweil-Pettis integrable selector and a Pettisintegrable multifunction. Now, we prove that the same result can beachieved in case of an arbitrary Banach space. Moreover we show thatan analogous result holds true also for the Denjoy-Khintchine-Pettisintegrable multifunctions. Applying the representation theorem wedescribe the multipliers of HKP and DKP integrable functions. Thenwe use this description to obtain an operator characterization ofHKP and DKP integrability.
Lingua originaleEnglish
Titolo della pubblicazione ospiteVector Measures, Integration and Related Topics
Pagine171-182
Numero di pagine12
Stato di pubblicazionePublished - 2010

Serie di pubblicazioni

NomeOperator Theory: Advances and Applications

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