Cobos, Fernando and Fernández-Cabrera, Luz M. and Martínez, Antón
(2006)
*On interpolation of Banach algebras and factorization of weakly compact homomorphisms.*
Bulletin des Sciences Mathematiques, 130
(7).
pp. 637-645.
ISSN 0007-4497

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Official URL: http://www.sciencedirect.com/science/article/pii/S000744970600008X

## Abstract

We show a necessary and sufficient condition on the lattice Γ for the general real method (· , ·)Γ to

preserve the Banach-algebra structure. As an application we derive factorization of weakly compact homomorphisms

through interpolation properties of weakly compact operators.

Item Type: | Article |
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Uncontrolled Keywords: | Real Interpolation; Operator; Spaces; Real Interpolation; Banach Algebras; Factoring Weakly Compact Homomorphisms; Mathematics, Applied |

Subjects: | Sciences > Mathematics > Functional analysis and Operator theory |

ID Code: | 15018 |

References: | [1] J. Bergh, J. Löfström, Interpolation Spaces. An Introduction, Springer, Berlin, 1976. [2] E.A. Bishop, Holomorphic completion, analytic continuation, and the interpolation of seminorms, Ann. Math. 78 (1963) 468–500. [3] A. Blanco, S. Kaijser, T.J. Ransford, Real interpolation of Banach algebras and factorization of weakly compact homomorphisms, J. Funct. Anal. 217 (2004) 126–141. [4] Y. Brudnyˇı, N. Krugljak, Interpolation Functors and Interpolation Spaces, vol. 1, North-Holland, Amsterdam, 1991. [5] A.P. Calderón, Intermediate spaces and interpolation, the complex method, Studia Math. 24 (1964) 113–190. [6] F. Cobos, Some spaces in which martingale difference sequences are unconditional, Bull. Polish Acad. Sci. Math. 34 (1986) 695–703. [7] F. Cobos, L.M. Fernández-Cabrera, A. Manzano, A. Martínez, Real interpolation and closed operator ideals, J. Math. Pures Appl. 83 (2004) 417–432. [8] F. Cobos, L.M. Fernández-Cabrera, A. Manzano, A. Martínez, On interpolation of Asplund operators, Math. Z. 250 (2005) 267–277. [9] F. Cobos, J. Peetre, L.E. Persson, On the connection between real and complex interpolation of quasi-Banach spaces, Bull. Sci. Math. 122 (1998) 17–37. [10] J.B. Conway, A Course in Functional Analysis, Springer, New York, 1990. [11] M. Cwikel, J. Peetre, Abstract K and J spaces, J. Math. Pures Appl. 60 (1981) 1–50. [12] W.J. Davis, T. Figiel, W.B. Johnson, A. Pelczy´nski, Factoring weakly compact operators, J. Funct. Anal. 17 (1974) 311–327. [13] J.E. Galé, T.J. Ransford, M.C. White, Weakly compact homomorphisms, Trans. Amer. Math. Soc. 331 (1992) 815– 824. [14] S. Kaijser, Interpolation of Banach algebras and open sets, Integral Equations Oper. Theory 41 (2001) 189–222. [15] M. Levy, L’espace d’interpolation réel (A0,A1)θ,p contient _p, C. R. Acad. Sci. Paris Sér. A 289 (1979) 675–677. [16] J. Lindenstrauss, L. Tzafriri, Classical Banach Spaces, I and II, Springer, New York, 1979. [17] M.A. Naimark, Normed Rings, P. Noordhoff N.V., Groningen, 1964. [18] N.K. Nikolskii, Spectral synthesis for a shift operator and zeros in certain classes of analytic functions smooth up to the boundary, Dokl. Akad. Nauk SSSR 190 (1970) 780–783. [19] P. Nilsson, Reiteration theorems for real interpolation and approximation spaces, Ann. Mat. Pura Appl. 132 (1982) 291–330. [20] P. Nilsson, Interpolation of Calderón and Ovchinnikov pairs, Ann. Mat. Pura Appl. 134 (1983) 201–332. [21] J. Peetre, A theory of interpolation of normed spaces, Notes Mat. 39 (1968) 1–86. Lecture Notes, Brasilia, 1963. [22] H. Triebel, Interpolation Theory, Function Spaces, Differential Operators, North-Holland, Amsterdam, 1978. [23] M. Zafran, The dichotomy problem for homogeneous Banach algebras, Ann. Math. 108 (1978) 97–105. |

Deposited On: | 26 Apr 2012 08:21 |

Last Modified: | 06 Feb 2014 10:14 |

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