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Linearization of functions

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Abstract

Given a space (U) of functions f:U → which are continuous, we construct another space *(U) and a map e:U→ *(U) linearizing all functions f∈ (U) (i.e. there are L f ∈ * (U)’ such that L f ^e=f). Such linearizations are stronger than mere preduals for (U), for example for (U)=ℓ1, linearizations correspond to preduals of ℓ1 which are isomorphic to c 0 . We also address the vector-valued case. A number of such linearizing constructions are to be found in the literarture, mostly for certain spaces of holomorphic functions. The procedure presented here generalizes all these special cases.

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Authors and Affiliations

  1. Depto. de Matemática, Universidad de San Andrés, Vito Dumas 284 (B1644BID) Victoria, Buenos Aires, Argentina

    Daniel Carando

  2. Depto. de Matemática, Universidad Torcuato Di Tella, Minones 2159/77 (C1428ATG), Buenos Aires, Argentina

    Ignacio Zalduendo

Authors
  1. Daniel Carando
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  2. Ignacio Zalduendo
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Mathematics Subject Classification (2000):46E10, 46G20

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Carando, D., Zalduendo, I. Linearization of functions. Math. Ann. 328, 683–700 (2004). https://doi.org/10.1007/s00208-003-0502-1

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  • DOI: https://doi.org/10.1007/s00208-003-0502-1

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