Function theoretic results for complex interpolation families of Banach spaces
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- by Richard Rochberg PDF
- Trans. Amer. Math. Soc. 284 (1984), 745-758 Request permission
Abstract:
The theory of complex interpolation of Banach spaces is viewed as a branch of the theory of vector valued holomorphic functions. Versions of the Schwarz lemma, Liouville’s theorem, the identity theorem and the reflection principle are proved and are interpreted from the point of view of interpolation theory.References
- Jöran Bergh and Jörgen Löfström, Interpolation spaces. An introduction, Grundlehren der Mathematischen Wissenschaften, No. 223, Springer-Verlag, Berlin-New York, 1976. MR 0482275
- Paul L. Butzer and Hubert Berens, Semi-groups of operators and approximation, Die Grundlehren der mathematischen Wissenschaften, Band 145, Springer-Verlag New York, Inc., New York, 1967. MR 0230022
- R. Coifman, M. Cwikel, R. Rochberg, Y. Sagher, and G. Weiss, Complex interpolation for families of Banach spaces, Harmonic analysis in Euclidean spaces (Proc. Sympos. Pure Math., Williams Coll., Williamstown, Mass., 1978) Proc. Sympos. Pure Math., XXXV, Part, Amer. Math. Soc., Providence, R.I., 1979, pp. 269–282. MR 545314
- R. R. Coifman, R. Rochberg, G. Weiss, M. Cwikel, and Y. Sagher, The complex method for interpolation of operators acting on families of Banach spaces, Euclidean harmonic analysis (Proc. Sem., Univ. Maryland, College Park, Md., 1979) Lecture Notes in Math., vol. 779, Springer, Berlin, 1980, pp. 123–153. MR 576042
- 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), no. 3, 203–229. MR 648799, DOI 10.1016/0001-8708(82)90034-2
- S. G. Kreĭn and Ju. I. Petunin, Scales of Banach spaces, Uspehi Mat. Nauk 21 (1966), no. 2 (128), 89–168 (Russian). MR 0193499
- Aleksander Pełczyński, Geometry of finite-dimensional Banach spaces and operator ideals, Notes in Banach spaces, Univ. Texas Press, Austin, Tex., 1980, pp. 81–181. MR 606222
- Richard Rochberg, Interpolation of Banach spaces and negatively curved vector bundles, Pacific J. Math. 110 (1984), no. 2, 355–376. MR 726495
- Richard Rochberg and Guido Weiss, Derivatives of analytic families of Banach spaces, Ann. of Math. (2) 118 (1983), no. 2, 315–347. MR 717826, DOI 10.2307/2007031
- Thomas H. Wolff, A note on interpolation spaces, Harmonic analysis (Minneapolis, Minn., 1981) Lecture Notes in Math., vol. 908, Springer, Berlin-New York, 1982, pp. 199–204. MR 654187
- Misha Zafran, Spectral theory and interpolation of operators, J. Functional Analysis 36 (1980), no. 2, 185–204. MR 569253, DOI 10.1016/0022-1236(80)90099-3
Additional Information
- © Copyright 1984 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 284 (1984), 745-758
- MSC: Primary 46M35; Secondary 30C80, 32A40, 46E40
- DOI: https://doi.org/10.1090/S0002-9947-1984-0743742-6
- MathSciNet review: 743742