The Aron‐Berner extension, Goldstine's theorem and <i>P</i>‐continuity

García, Rubén J.; Jaramillo, Jesús Á.; Llavona, José Luis González

doi:10.1002/mana.200810120

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Extension and Lifting Of Polynomials And Holomorphic Mappings1

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2011

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“…We will use the notation AB(P ) = P . Different descriptions of the Aron-Berner extension can be seen in [2,11,22,40]. The operator AB is a section for the restriction operator R : P( n X) → P( n Y ).…”

Section: Extension and Lifting Of Polynomials And Holomorphic Mappingsmentioning

confidence: 99%

Extension and Lifting of Operators and Polynomials

Castillo

García

Suárez³

2011

Mediterr. J. Math.

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Abstract. We study the problem of extension and lifting of operators belonging to certain operator ideals, as well as that of their associated polynomials and holomorphic functions. Our results provide a characterization of L 1 and L∞-spaces that includes and extends those of Lindenstrauss-Rosenthal [32] using compact operators and González-Gutiérrez [23] using compact polynomials. We display several examples to show the difference between extending and lifting compact (resp. weakly compact, unconditionally convergent, separable and Rosenthal) operators to operators of the same type. Finally, we show the previous results in a homological perspective, which helps the interested reader to understand the motivations and nature of the results presented.

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Section: Extension and Lifting Of Polynomials And Holomorphic Mappingsmentioning

confidence: 99%