Injective factorization of holomorphic mappings
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- by Manuel González and Joaquín M. Gutiérrez PDF
- Proc. Amer. Math. Soc. 127 (1999), 1715-1721 Request permission
Erratum: Proc. Amer. Math. Soc. 129 (2001), 1255-1256.
Abstract:
We characterize the holomorphic mappings $f$ between complex Banach spaces that may be written in the form $f=g\circ T$, where $g$ is another holomorphic mapping and $T$ is an operator belonging to a closed injective operator ideal. Analogous results are previously obtained for multilinear mappings and polynomials.References
- R. M. Aron and P. Galindo, Weakly compact multilinear mappings, Proc. Edinburgh Math. Soc. 40 (1997), 181–192.
- R. M. Aron, C. Hervés, and M. Valdivia, Weakly continuous mappings on Banach spaces, J. Functional Analysis 52 (1983), no. 2, 189–204. MR 707203, DOI 10.1016/0022-1236(83)90081-2
- R. M. Aron and J. B. Prolla, Polynomial approximation of differentiable functions on Banach spaces, J. Reine Angew. Math. 313 (1980), 195–216. MR 552473, DOI 10.1515/crll.1980.313.195
- Seán Dineen, Complex analysis in locally convex spaces, Notas de Matemática [Mathematical Notes], vol. 83, North-Holland Publishing Co., Amsterdam-New York, 1981. MR 640093
- Seán Dineen, Entire functions on $c_{0}$, J. Funct. Anal. 52 (1983), no. 2, 205–218. MR 707204, DOI 10.1016/0022-1236(83)90082-4
- Stefan Geiss, Ein Faktorisierungssatz für multilineare Funktionale, Math. Nachr. 134 (1987), 149–159 (German). MR 918674, DOI 10.1002/mana.19871340110
- Manuel González and Joaquín M. Gutiérrez, Factorization of weakly continuous holomorphic mappings, Studia Math. 118 (1996), no. 2, 117–133. MR 1389759
- Manuel González, Joaquín M. Gutiérrez, and José G. Llavona, Polynomial continuity on $l_1$, Proc. Amer. Math. Soc. 125 (1997), no. 5, 1349–1353. MR 1371124, DOI 10.1090/S0002-9939-97-03733-7
- Hans Jarchow, Locally convex spaces, Mathematische Leitfäden. [Mathematical Textbooks], B. G. Teubner, Stuttgart, 1981. MR 632257, DOI 10.1007/978-3-322-90559-8
- Hans Jarchow, On certain locally convex topologies on Banach spaces, Functional analysis: surveys and recent results, III (Paderborn, 1983) North-Holland Math. Stud., vol. 90, North-Holland, Amsterdam, 1984, pp. 79–93. MR 761374, DOI 10.1016/S0304-0208(08)71468-3
- Hans Jarchow, Weakly compact operators on $C(K)$ and $C^*$-algebras, Functional analysis and its applications (Nice, 1986) ICPAM Lecture Notes, World Sci. Publishing, Singapore, 1988, pp. 263–299. MR 979519
- H. Jarchow and U. Matter, On weakly compact operators on $C(K)$-spaces, in: N. Kalton and E. Saab (eds.), Banach Spaces (Proc., Missouri 1984), Lecture Notes in Math. 1166, Springer, Berlin 1985, 80–88.
- Jorge Mujica, Complex analysis in Banach spaces, North-Holland Mathematics Studies, vol. 120, North-Holland Publishing Co., Amsterdam, 1986. Holomorphic functions and domains of holomorphy in finite and infinite dimensions; Notas de Matemática [Mathematical Notes], 107. MR 842435
- Albrecht Pietsch, Operator ideals, North-Holland Mathematical Library, vol. 20, North-Holland Publishing Co., Amsterdam-New York, 1980. Translated from German by the author. MR 582655
Additional Information
- Manuel González
- Affiliation: Departamento de Matemáticas, ETS de Ingenieros Industriales, Universidad Politéc- nica de Madrid, C. José Gutiérrez Abascal 2, 28006 Madrid, Spain
- MR Author ID: 219505
- Email: gonzalem@ccaix3.unican.es
- Joaquín M. Gutiérrez
- Affiliation: Departamento de Matemáticas, ETS de Ingenieros Industriales, Universidad Politéc- nica de Madrid, C. José Gutiérrez Abascal 2, 28006 Madrid, Spain
- MR Author ID: 311216
- Email: jgutierrez@math.etsii.upm.es
- Received by editor(s): September 10, 1997
- Published electronically: February 11, 1999
- Additional Notes: The first author was supported in part by DGICYT Grant PB 97–0349 (Spain).
The second author was supported in part by DGICYT Grant PB 96–0607 (Spain). - Communicated by: Dale Alspach
- © Copyright 1999 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 127 (1999), 1715-1721
- MSC (1991): Primary 46G20; Secondary 47D50
- DOI: https://doi.org/10.1090/S0002-9939-99-04917-5
- MathSciNet review: 1610897