Extension of Pettis integration: Pettis operators and their integrals

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...

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Veröffentlicht in:	Collectanea mathematica (Barcelona) 2019-08, Vol.70 (2), p.267-281
Hauptverfasser:	Blasco, Oscar, Drewnowski, Lech
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Sprache:	eng
Schlagworte:	Algebra Analysis Analytic functions Applications of Mathematics Banach spaces Geometry Harmonic functions Integrals Linear operators Mathematics Mathematics and Statistics Operators (mathematics)
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description	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.
doi_str_mv	10.1007/s13348-018-0225-y
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title	Extension of Pettis integration: Pettis operators and their integrals
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