Complex interpolation and geometry of Banach spaces

Springer Science and Business Media LLC - Tập 136 - Trang 317-328 - 1984
Mario Milman1
1USA

Tóm tắt

The coincidence of the real and complex methods of interpolation is investigated. Positive results are established under the presence of geometrical properties which are expressed in terms of vector valued Fourier transforms. The results are applied to complex interpolation of Hp spaces and to the study of geometrical properties of Banach spaces.

Tài liệu tham khảo

R. Adams,Sobolev Spaces, Academic Press, New York, 1975.

J. Berg -J. Lofstrom,Interpolation Spaces. An Introduction, Springer, Berlin, 1976.

J. Diestel -J. Uhl,Vector measures, Math. Surveys No. 15, Amer. Math. Soc., Providence, 1977.

I. C.Gohberg - M. G.Krein,Introduction to the theory of linear non-self adjoint operators in Hilbert space, Moscow, 1965.

J. P. Kahane,Series de Fourier absolument convergentes, Springer, Berlin, 1970.

J. L. Lions -J. Peetre,Sur une classe d'Espaces d'Interpolation, Inst. Hautes Études Sci. Publ. Math.,19 (1964), pp. 5–68.

Ch. McCarthy, cp, Israel J. Math.,5 (1967), pp. 249–271.

M.Milman,Interpolation of some concrete scales of spaces, Technical report, Lund, 1982.

J. Peetre,Sur la transformation de Fourier des functions à valeurs vectorielles, Rend. Sem. Mat. Univ. Padova,42 (1969), pp. 15–26.

N. Tomczak-Jaegermann,The moduli of smoothness and convexity and the Rademacher averages of trace classes S p(1⩽p<∞), Studia Math.,50 (1974), pp. 163–182.

L. R. Williams -J. H. Wells,L p inequalities, J. Math. Anal. Appl.,64 (1978), pp. 518–529.