Extension of Pettis integration: Pettis operators and their integrals

• Autores: Óscar Blasco de la Cruz , Lech Drewnowski
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 70, Fasc. 2, 2019, págs. 267-281
• Idioma: inglés
• DOI: 10.1007/s13348-018-0225-y
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• Resumen

  • In this note, the authors discuss the concepts of a Pettis operator, by which they mean a weak ^*–weakly continuous linear operator F from a dual Banach space to an L_1-space, and of its Pettis integral, understood simply as the dual operator F^* of F. Applications to radial limits in weak Hardy spaces of vector-valued harmonic and holomorphic functions are provided.