Real interpolation for families of Banach spaces

Maria Carro

Studia Mathematica (1994)

  • Volume: 109, Issue: 1, page 1-21
  • ISSN: 0039-3223

Abstract

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We develop a new method of real interpolation for infinite families of Banach spaces that covers the methods of Lions-Peetre, Sparr for N spaces, Fernández for 2 N spaces and the recent method of Cobos-Peetre.

How to cite

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Carro, Maria. "Real interpolation for families of Banach spaces." Studia Mathematica 109.1 (1994): 1-21. <http://eudml.org/doc/216057>.

@article{Carro1994,
abstract = {We develop a new method of real interpolation for infinite families of Banach spaces that covers the methods of Lions-Peetre, Sparr for N spaces, Fernández for $2^N$ spaces and the recent method of Cobos-Peetre.},
author = {Carro, Maria},
journal = {Studia Mathematica},
keywords = {real interpolation for infinite families of Banach spaces},
language = {eng},
number = {1},
pages = {1-21},
title = {Real interpolation for families of Banach spaces},
url = {http://eudml.org/doc/216057},
volume = {109},
year = {1994},
}

TY - JOUR
AU - Carro, Maria
TI - Real interpolation for families of Banach spaces
JO - Studia Mathematica
PY - 1994
VL - 109
IS - 1
SP - 1
EP - 21
AB - We develop a new method of real interpolation for infinite families of Banach spaces that covers the methods of Lions-Peetre, Sparr for N spaces, Fernández for $2^N$ spaces and the recent method of Cobos-Peetre.
LA - eng
KW - real interpolation for infinite families of Banach spaces
UR - http://eudml.org/doc/216057
ER -

References

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  1. [BL] J. Bergh and J. Löfström, Interpolation Spaces. An Introduction, Springer, Berlin, 1976. Zbl0344.46071
  2. [C] A. P. Calderón, Intermediate spaces and interpolation, the complex method, Studia Math. 24 (1964), 113-190. Zbl0204.13703
  3. [CP] F. Cobos and J. Peetre, Interpolation of compact operators: the multidimensional case, Proc. London Math. Soc. (3) 63 (1991), 371-400. Zbl0702.46047
  4. [CCRSW] R. R. Coifman, M. Cwikel, R. Rochberg, Y. Sagher and G. Weiss, A theory of complex interpolation for families of Banach spaces, Adv. in Math. 43 (1982), 203-229. Zbl0501.46065
  5. [CJ] M. Cwikel and S. Janson, Real and complex interpolation methods for finite and infinite families of Banach spaces, ibid. 66 (1987), 234-290. Zbl0646.46070
  6. [F] D. L. Fernández, Interpolation of 2 d Banach spaces and the Calderón spaces X(E), Proc. London Math. Soc. (3) 56 (1988), 143-162. Zbl0662.46077
  7. [G] J. B. Garnett, Bounded Analytic Functions, Academic Press, New York, 1981. Zbl0469.30024
  8. [GU] J. Gustavsson, A function parameter in connection with interpolation of Banach spaces, Math. Scand. 42 (1978), 289-305. Zbl0389.46024
  9. [LP] J. L. Lions et J. Peetre, Sur une classe d'espaces d'interpolation, Inst. Hautes Études Sci. Publ. Math. 19 (1964), 5-68. 
  10. [M] M. Mastyło, The K-functional for a Banach couple ( Ᾱ ∂ E 0 ; K , Ᾱ ∂ E 1 ; K ) , Comment. Math. 25 (1985), 93-108. 
  11. [P] J. Peetre, A theory of interpolation of normed spaces, Lecture notes, Brasilia (Notas de matemática 39, 1968) (1963), 1-86. 
  12. [S] G. Sparr, Interpolation of several Banach spaces, Ann. Mat. Pura Appl. 99 (1974), 247-316. Zbl0282.46022

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