RESEARCH ARTICLE

Complex interpolation and Calderón product of quasi-Banach spaces

  • Wen YUAN
Expand
  • School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875, China

Received date: 13 Nov 2014

Accepted date: 11 Apr 2016

Published date: 17 May 2016

Copyright

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg

Abstract

We prove that the inner complex interpolation of two quasi-Banach lattices coincides with the closure of their intersection in their Calderón product. This generalizes a classical result by V. A. Shestakov in 1974 for Banach lattices.

Cite this article

Wen YUAN . Complex interpolation and Calderón product of quasi-Banach spaces[J]. Frontiers of Mathematics in China, 2016 , 11(3) : 753 -762 . DOI: 10.1007/s11464-016-0541-z

1
Calderón A P. Intermediate spaces and interpolation, the complex method. Studia Math, 1964, 24: 113–190

2
Janson S. Minimal and maximal methods of interpolation. J Funct Anal, 1981, 44: 50–73

DOI

3
Kalton N. Plurisubharmonic functions on quasi-Banach spaces. Studia Math, 1986, 84: 297–324

4
Kalton N, Mayboroda S, Mitrea M. Interpolation of Hardy-Sobolev-Besov-Triebel-Lizorkin spaces and applications to problems in partial differential equations. In: De Carli L, Milman M, eds. Interpolation Theory and Applications. Contemp Math, Vol 445. Providence: Amer Math Soc, 2007, 121–177

DOI

5
Kalton N, Mitrea M. Stability results on interpolation scales of quasi-Banach spaces and applications. Trans Amer Math Soc, 1998, 350: 3903–3922

DOI

6
Lu Y, Yang D, Yuan W. Interpolation of Morrey spaces on metric measure spaces. Canad Math Bull, 2014, 57: 598–608

DOI

7
Nilsson P. Interpolation of Banach lattices. Studia Math, 1985, 82: 133–154

8
Peetre J. Sur l’utilisation des suites inconditionellement sommables dans la théorie des espaces d’interpolation. Rend Sem Mat Univ Padova, 1971, 46: 173–190

9
Shestakov V A. Interpolation of linear operators in spaces of measurable functions. Funktsional Anal i Prilozhen, 1974, 8: 91–92 (in Russian)

10
Shestakov V A. On complex interpolation of Banach spaces of measurable functions. Vestnik Leningrad Univ, 1974, 19: 64–68 (in Russian)

11
Yuan W, Sickel W, Yang D. Interpolation of Morrey-Campanato and related smoothness spaces. Sci China Math, 2015, 58: 1835–1908

DOI

Outlines

/