On the Relationship between Interpolation of Banach Algebras and Interpolation of Bilinear Operators
Canadian mathematical bulletin, Tome 53 (2010) no. 1, pp. 51-57

Voir la notice de l'article provenant de la source Cambridge University Press

We show that if the general real method ${{\left( \cdot \,,\,\cdot\right)}_{\Gamma }}$ preserves the Banach-algebra structure, then a bilinear interpolation theorem holds for ${{\left( \cdot \,,\,\cdot\right)}_{\Gamma }}$ .
DOI : 10.4153/CMB-2010-009-1
Mots-clés : 46B70, 46M35, 46H05, real interpolation, bilinear operators, Banach algebras
Cobos, Fernando; Fernández-Cabrera, Luz M. On the Relationship between Interpolation of Banach Algebras and Interpolation of Bilinear Operators. Canadian mathematical bulletin, Tome 53 (2010) no. 1, pp. 51-57. doi: 10.4153/CMB-2010-009-1
@article{10_4153_CMB_2010_009_1,
     author = {Cobos, Fernando and Fern\'andez-Cabrera, Luz M.},
     title = {On the {Relationship} between {Interpolation} of {Banach} {Algebras} and {Interpolation} of {Bilinear} {Operators}},
     journal = {Canadian mathematical bulletin},
     pages = {51--57},
     year = {2010},
     volume = {53},
     number = {1},
     doi = {10.4153/CMB-2010-009-1},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2010-009-1/}
}
TY  - JOUR
AU  - Cobos, Fernando
AU  - Fernández-Cabrera, Luz M.
TI  - On the Relationship between Interpolation of Banach Algebras and Interpolation of Bilinear Operators
JO  - Canadian mathematical bulletin
PY  - 2010
SP  - 51
EP  - 57
VL  - 53
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2010-009-1/
DO  - 10.4153/CMB-2010-009-1
ID  - 10_4153_CMB_2010_009_1
ER  - 
%0 Journal Article
%A Cobos, Fernando
%A Fernández-Cabrera, Luz M.
%T On the Relationship between Interpolation of Banach Algebras and Interpolation of Bilinear Operators
%J Canadian mathematical bulletin
%D 2010
%P 51-57
%V 53
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-2010-009-1/
%R 10.4153/CMB-2010-009-1
%F 10_4153_CMB_2010_009_1

[1] [1] Bergh, J. and Löfström, J., Interpolation spaces. An introduction. Grundlehren der Mathematischen Wissenschaften 223, Springer-Verlag, Berlin-New York, 1976. Google Scholar

[2] [2] Bishop, E. A., Holomorphic completion, analytic continuation, and the interpolation of semi-norms. Ann. of Math. 78(1963), 468–500. doi:10.2307/1970537 Google Scholar

[3] [3] Blanco, A., Kaijser, S., and Ransford, T. J., Real interpolation of Banach algebras and factorization of weakly compact homomorphisms. J. Funct. Anal. 217(2004), no. 1, 126–141. doi:10.1016/j.jfa.2004.03.011 Google Scholar

[4] [4] Brudnyĭ, Y. and Krugljak, N., Interpolation functors and interpolation spaces. Vol. 1. North-Holland Mathematical Library 47, North-Holland Publishing Co., Amsterdam, 1991. Google Scholar

[5] [5] Calder ón, A.-P., Intermediate spaces and interpolation, the complex method. Studia Math. 24(1964), 113–190. Google Scholar

[6] [6] Cobos, F., Fernández-Cabrera, L. M., and Martínez, A., Compact operators between K- and J-spaces. Studia Math. 166(2005), no. 3, 199–220. doi:10.4064/sm166-3-1 Google Scholar

[7] [7] Cobos, F., Fernández-Cabrera, L. M., and Martínez, A., On interpolation of Banach algebras and factorization of weakly compact homomorphisms. Bull. Sci. Math. 130(2006), no. 7, 637–645. doi:10.1016/j.bulsci.2005.12.003 Google Scholar

[8] [8] Cobos, F., Fernández-Cabrera, L. M., and Martínez, A., Abstract K and J spaces and measure of non-compactness. Math. Nachr. 280(2007), no. 15, 1698–1708. doi:10.1002/mana.200510572 Google Scholar

[9] [9] Kaijser, S., Interpolation of Banach algebras and open sets, Integr. Equ. Oper. Theory 41(2001) 189–222. doi:10.1007/BF01295305 Google Scholar

[10] [10] Nilsson, P., Reiteration theorems for real interpolation and approximation spaces. Ann. Mat. Pura Appl. 132(1982), 291–330. doi:10.1007/BF01760986 Google Scholar

[11] [11] Nilsson, P., Interpolation of Calderón and Ovčhinnikov pairs. Ann. Mat. Pura Appl. 134(1983), 201–232. doi:10.1007/BF01773505 Google Scholar

[12] [12] Peetre, J., A theory of interpolation of normed spaces. Notas de Matemática 39, Instituto de Matemática Pura e Aplicada, Conselho Nacional de Pesquisas, Rio de Janeiro, 1968. Google Scholar

[13] [13] Triebel, H., Interpolation theory, function spaces, differential operators. North-Holland Mathematical Library 18, North-Holland Publishing Co., Amsterdam-New York, 1978. Google Scholar

[14] [14] Zafran, M., The dichotomy problem for homogeneous Banach algebras. Ann. of Math. 108(1978), no. 1, 97–105. doi:10.2307/1970931 Google Scholar

Cité par Sources :