|
Polynomials generated by linear operators
Author(s):
P.
Galindo;
M.
L.
Lourenço;
L.
A.
Moraes
Journal:
Proc. Amer. Math. Soc.
132
(2004),
2917-2927.
MSC (2000):
Primary 46G20
Posted:
June 2, 2004
Retrieve article in:
PDF DVI PostScript
Abstract |
References |
Similar articles |
Additional information
Abstract:
We study the class of Banach algebra-valued  -homogeneous polynomials generated by the  powers of linear operators. We compare it with the finite type polynomials. We introduce a topology  on  similar to the weak topology, to clarify the features of these polynomials.
References:
-
- 1.
- R.M. Aron and P. Berner, A Hahn-Banach theorem for analytic mappings, Bull. Soc. Math. France 106 (1978), 3-24. MR 80e:46029
- 2.
- R.M. Aron, B.J. Cole and T.W. Gamelin, Weak-star continuous analytic functions, Canad. J. Math. 47 (4) (1995), 673-683. MR 96d:46060
- 3.
- R.M. Aron and M. Schottenloher, Compact holomorphic mappings on Banach spaces and the approximation property, J. Functional Anal. 21 (1976), 7-30. MR 53:6323
- 4.
- N. Bourbaki, Éléments de mathématique. Topologie Générale, Hermann, Paris (1971). MR 50:11111
- 5.
- J. Duncan and S.A.R. Hosseinium,The second dual of a Banach algebra, Proc. Roy. Soc. Edinburgh 84A (1979), 309-325. MR 81f:46057
- 6.
- S. Dineen, Complex Analysis on Infinite Dimensional Spaces, Springer (1999). MR 2001a:46043
- 7.
- N. Dunford and J. Schwartz, Linear Operators, Part I, Interscience (1958). MR 22:8302
- 8.
- M. González and J. Gutiérrez, Polynomial Grothendieck properties, Glasgow Math. J. 37 (1995), 211-219. MR 96h:46025
- 9.
- M. González and J. Gutiérrez, The compact weak topology on a Banach space, Proc. Roy. Soc. Edinburgh 120A (1992), 367-379. MR 93c:46022
- 10.
- J. Gómez, On local convexity of bounded weak topologies on Banach spaces, Pacific J. Math. 110 (1984), 71-76. MR 85a:46014
- 11.
- J. R. Holub, Reflexivity of
 Proc. Amer. Math. Soc. 39 (1) (1973), 175-177. MR 47:3956 - 12.
- M. L. Lourenço and L. A. Moraes, A class of polynomials from Banach spaces into Banach algebras, Publ. Res. Inst. Math. Sci., Kyoto Univ. 37 (2001), 521-529. MR 2002k:46110
- 13.
- J. Mujica, Reflexive spaces of homogeneous polynomials, Bull. Polish Acad. of Sci. 49 (3) (2001), 211-222. MR 2002i:46019
- 14.
- R. Ryan, Weakly compact holomorphic mappings on Banach spaces, Pacific J. Math. 131 (1988), 179-190 MR 89a:46103
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical Society
with MSC
(2000):
46G20
Retrieve articles in all Journals with MSC
(2000):
46G20
Additional Information:
P.
Galindo
Affiliation:
Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Valencia 46.100, Burjasot-Valencia, Spain
Email:
Pablo.Galindo@uv.es
M.
L.
Lourenço
Affiliation:
Departamento de Matemática, Instituto de Matemática e Estatística, Universidade de São Paulo, Caixa Postal 66281 - CEP : 05315-970, São Paulo, Brazil
Email:
mllouren@ime.usp.br
L.
A.
Moraes
Affiliation:
Instituto de Matemática, Universidade Federal do Rio de Janeiro, CP 68530 - CEP: 21945-970, Rio de Janeiro, Brazil
Email:
luiza@im.ufrj.br
DOI:
10.1090/S0002-9939-04-07442-8
PII:
S 0002-9939(04)07442-8
Keywords:
$n$-homogeneous polynomials,
linear operator,
Arens product
Received by editor(s):
September 4, 2002
Posted:
June 2, 2004
Additional Notes:
The first author was supported by CCInt-USP and FAPEMIG
The second author was supported in part by agreement USP/UV and FAPESP
The third author was supported in part by CNPq, Research Grant 300016/82-4 and PROAP/UFRJ
Communicated by:
Jonathan M. Borwein
Copyright of article:
Copyright
2004,
American Mathematical Society
|
Comments: webmaster@ams.org