Holomorphic functions and polynomial ideals on Banach spaces

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Given a multiplicative sequence of polynomial ideals, we consider the associated algebra of holomorphic functions of bounded type. We prove that, under very natural conditions satisfied by many usual classes of polynomials, the spectrum of this algebra "behaves" like the classical case of...

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Autor principal: Carando, D.
Otros Autores: Dimant, V., Muro, S.
Formato: Capítulo de libro
Lenguaje:Inglés
Publicado: 2012
Acceso en línea:Registro en Scopus
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100 1 |a Carando, D. 
245 1 0 |a Holomorphic functions and polynomial ideals on Banach spaces 
260 |c 2012 
270 1 0 |m Dimant, V.; Departamento de Matemática, Universidad de San Andrés, Vito Dumas 284, Victoria, B1644BID Buenos Aires, Argentina; email: vero@udesa.edu.ar 
506 |2 openaire  |e Política editorial 
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504 |a Aron, R.M., Cole, B.J., Gamelin, T.W., Weak-star continuous analytic functions (1995) Can. J. Math., 47, pp. 673-683 
504 |a Aron, R.M., Galindo, P., García, D., Maestre, M., Regularity and algebras of analytic functions in infinite dimensions (1996) Trans. Am. Math. Soc., 348, pp. 543-559 
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504 |a Carando, D., Extendible polynomials on Banach spaces (1999) J. Math. Anal. Appl., 233, pp. 359-372 
504 |a Carando, D., Extendibility of polynomials and analytic functions on l p (2001) Studia Math., 145, pp. 63-73 
504 |a Carando, D., Dimant, V., Duality in spaces of nuclear and integral polynomials, J (2000) Math. Anal. Appl., 241, pp. 107-121 
504 |a Carando, D., Dimant, V., Muro, S., Hypercyclic convolution operators on Fréchet spaces of analytic functions (2007) J. Math. Anal. Appl., 336, pp. 1324-1340 
504 |a Carando, D., Dimant, V., Muro, S., Coherent sequences of polynomial ideals on Banach spaces (2009) Math. Nachr., 282, pp. 1111-1133 
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504 |a Carando, D., García, D., Maestre, M., Homomorphisms and composition operators on algebras of analytic functions of bounded type (2005) Adv. Math., 197, pp. 607-629 
504 |a Carando, D., Lassalle, S., E′ and its relation with vector-valued functions on E (2004) Ark. Mat., 42, pp. 283-300 
504 |a Carando, D., Zalduendo, I., A Hahn-Banach theorem for integral polynomials (1999) Proc. Am. Math. Soc., 127, pp. 241-250 
504 |a Davie, A.M., Gamelin, T.W., A theorem on polynomial-star approximation (1988) Proc. Am. Math. Soc., 106, pp. 351-356 
504 |a Defant, A., Floret, K., (1993) Tensor Norms and Operator Ideals, 176. , North-Holland: North-Holland Mathematics Studies 
504 |a Dimant, V., Galindo, P., Maestre, M., Zalduendo, I., Integral holomorphic functions (2004) Studia Math., 160, pp. 83-99 
504 |a Dineen, S., (1999) Complex Analysis on Infinite Dimensional Spaces. Springer Monographs in Mathematics, , London: Springer 
504 |a Dineen, S., Holomorphy types on a Banach space (1971) Studia Math., 39, pp. 241-288 
504 |a Floret, K., Natural norms on symmetric tensor products of normed spaces (1997) Note Mat., 17, pp. 153-188 
504 |a Floret, K., Minimal ideals of n-homogeneous polynomials on Banach spaces (2001) Results Math., 39, pp. 201-217 
504 |a Floret, K., On ideals of n-homogeneous polynomials on Banach spaces (2002) Topological algebras with applications to differential geometry and mathematical physics (Athens, 1999), pp. 19-38. , University Athens, Athens 
504 |a Floret, K., Hunfeld, S., Ultrastability of ideals of homogeneous polynomials and multilinear mappings on Banach spaces (2002) Proc. Am. Math. Soc., 130, pp. 1425-1435 
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504 |a Harris, L.A., A Bernstein-Markov theorem for normed spaces (1997) J. Math. Anal. Appl., 208, pp. 476-486 
504 |a Lassalle, S., Zalduendo, I., To what extent does the dual Banach space E′ determine the polynomials over E? (2000) Ark. Mat., 38, pp. 343-354 
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504 |a Mujica, J., Complex analysis in Banach spaces (1986) Holomorphic functions and domains of holomorphy in finite and infinite dimensions, 120. , North-Holland Mathematics Studies, North-Holland Publishing Co., Amsterdam 
504 |a Nachbin, L., (1969) Topology on Spaces of Holomorphic Mappings. Ergebnisse Der Mathematik Und Ihrer Grenzgebiete, Band 47, , New York: Springer 
520 3 |a Given a multiplicative sequence of polynomial ideals, we consider the associated algebra of holomorphic functions of bounded type. We prove that, under very natural conditions satisfied by many usual classes of polynomials, the spectrum of this algebra "behaves" like the classical case of M b(E) (the spectrum of H b(E), the algebra of bounded type holomorphic functions). More precisely, we prove that can be endowed with a structure of Riemann domain over E′′ and that the extension of each -holomorphic function of bounded type in each connected component. We also prove a Banach-Stone type theorem for these algebras. © 2010 Universitat de Barcelona.  |l eng 
593 |a Departamento de Matemática, Pab I, Facultad de Cs. Exactas y Naturales, Universidad de Buenos Aires, 1428 Buenos Aires, Argentina 
593 |a Departamento de Matemática, Universidad de San Andrés, Vito Dumas 284, Victoria, B1644BID Buenos Aires, Argentina 
690 1 0 |a HOLOMORPHIC FUNCTIONS 
690 1 0 |a POLYNOMIAL IDEALS 
690 1 0 |a RIEMANN DOMAINS OVER BANACH SPACES 
700 1 |a Dimant, V. 
700 1 |a Muro, S. 
773 0 |d 2012  |g v. 63  |h pp. 71-91  |k n. 1  |p Collect. Math.  |x 00100757  |t Collectanea Mathematica 
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856 4 0 |u https://doi.org/10.1007/s13348-010-0025-5  |y DOI 
856 4 0 |u https://hdl.handle.net/20.500.12110/paper_00100757_v63_n1_p71_Carando  |y Handle 
856 4 0 |u https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00100757_v63_n1_p71_Carando  |y Registro en la Biblioteca Digital 
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