Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Block diagonal polynomials

Authors: Verónica Dimant and Raquel Gonzalo
Journal: Trans. Amer. Math. Soc. 353 (2001), 733-747
MSC (2000): Primary 46G20; Secondary 46Bxx
Published electronically: October 13, 2000
MathSciNet review: 1804515
Full-text PDF

Abstract | References | Similar Articles | Additional Information


In this paper we introduce and study a certain class of polynomials in spaces with unconditional finite dimensional decomposition. Some applications to the existence of copies of $\ell _\infty $ in spaces of polynomials and to the stabilization of polynomial algebras are given.

References [Enhancements On Off] (What's this?)

  • 1. A. Arias and J. Farmer, On the structure of tensor products of $\ell _p$-spaces, Pacific. J. Math. 175, 1 (1996), 13-37. MR 98d:46015
  • 2. R. Aron and J. Globevnik, Analytic functions on $c_o$, Rev. Mat. Univ. Complut. Madrid 2 (1989), suppl., 27-33. MR 91d:46051
  • 3. R. Aron, C. Hervés and M. Valdivia, Weakly continuous mappings on Banach spaces, J. Funct. Anal. 52 (1983), 189-204. MR 84g:46066
  • 4. R. Aron and J. Prolla, Polynomial approximation of differentiable functions on Banach spaces, J. Reine Angew. Math. 3 (1980), 195-216. MR 81c:41078
  • 5. J. Bochnak and J. Siciak, Polynomials and multilinear mappings in topological vector spaces, Studia Math. 39 (1971), 59-76. MR 47:2364
  • 6. F. Bombal and M. Fernández-Unzueta, Polynomial convergence of sequences in Banach spaces, Rev. Acad. Cienc. Exact. Fís. Natur. Madrid, to appear.
  • 7. C. Boyd and R. Ryan, Bounded weak continuity of homogeneous polynomials at the origin, Arch. Math. (Basel) 71, 3 (1998), 211-218. MR 99k:46076
  • 8. J. Castillo, R. García and R. Gonzalo, Banach spaces in which all multilinear forms are weakly sequentially continuous, Studia Math. 136, 2 (1999), 121-145. CMP 2000:02
  • 9. V. Dimant and S. Dineen, Banach subspaces of spaces of holomorphic functions and related topics, Math. Scand. 83 (1998), 142-160. MR 99m:46031
  • 10. V. Dimant and I. Zalduendo, Bases in spaces of multilinear forms over Banach spaces, J. Math. Anal. Appl. 200 (1996), 548-566. MR 97k:96017
  • 11. S. Dineen, ``Complex analysis in locally convex spaces'', North Holland Math. Studies 57, 1981. MR 84b:46050
  • 12. S. Dineen, A Dvoretzky theorem for polynomials, Proc. Amer. Math. Soc. 123, (1995), 2817-2821. MR 95k:46021
  • 13. S. Dineen, ``Complex analysis on Infinite Dimensional Spaces'', Springer Monographs in Mathematics, 1999. CMP 99:17
  • 14. S. Dineen and M. Lindström, Spaces of homogeneous polynomials containing $c_0$ or $\ell _\infty $, on ``Functional Analysis'', de Gruyter, Berlin, 1996, p. 119-127. MR 97i:46083
  • 15. J. Farmer and W. Johnson, Polynomial Schur and polynomial Dunford-Pettis properties, Contemp. Math. 144 (1993), 95-105. MR 94e:46078
  • 16. R. Gonzalo, Multilinear forms, subsymmetric polynomials, and spreading models on Banach spaces, J. Math. Anal. Appl. 202 (1996), 379-397. MR 98a:46054
  • 17. R. Gonzalo, Upper and lower estimates in Banach sequence spaces, Comment. Math. Univ. Carolin. 36, 4 (1995), 641-653. MR 97d:46020
  • 18. R. Gonzalo, Smoothness and polynomials on Banach spaces, Doctoral Thesis, Universidad Complutense de Madrid, 1994.
  • 19. P. Hájek, Polynomial algebras on classical Banach spaces, Israel J. Math. 106 (1998), 209-220. MR 99k:46079
  • 20. F. Hernández and V. Peirats, Weighted sequence subspaces of Orlicz function spaces isomorphic to $\ell _p$, Arch. Math. (Basel) (1987), 270-280. MR 89c:46044
  • 21. J. R. Holub, Tensor product bases and tensor diagonals, Trans. Amer. Math. Soc. 151 (1970), 563-579. MR 43:5286
  • 22. J. Lindenstrauss and L. Tzafriri, ``Classical Banach spaces I'', Springer, 1977. MR 58:17766
  • 23. A. Nemirovski{\u{\i}}\kern.15emand S. Semenov, The polynomial approximation of functions on Hilbert spaces, Math. USSR-Sb 21 (1973), 255-273. MR 58:30211b
  • 24. K. Sundaresan, Geometry of spaces of homogeneous polynomials on Banach lattices, Applied geometry and discrete mathematics, 571-586, DIMACS Ser. Discrete Math. Theoret. Comput. Sci., 4, Amer. Math. Soc., Providence, RI, 1991. MR 92k:46077

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 46G20, 46Bxx

Retrieve articles in all journals with MSC (2000): 46G20, 46Bxx

Additional Information

Verónica Dimant
Affiliation: Departamento de Economía y Matemática, Universidad de San Andrés, Vito Dumas 284 (1644) Victoria, Prov. de Buenos Aires, Argentina

Raquel Gonzalo
Affiliation: Departamento de Análisis Matemático, Facultad de Ciencias Matemáticas, Universidad Complutense, 28040 Madrid, Spain
Address at time of publication: Departamento de Matemática Aplicada, Facultad de Informática, Universidad Politécnica, Campus de Montegancedo, 28660 Boadilla del Monte, Madrid, Spain

Keywords: Polynomials, weak sequential continuity, containment of $\ell_\infty$
Received by editor(s): July 24, 1998
Received by editor(s) in revised form: July 22, 1999
Published electronically: October 13, 2000
Additional Notes: The first author was partially supported by Instituto de Cooperación Iberoamericano, and the second author was partially supported by PGCYT PB-96-0607
Article copyright: © Copyright 2000 American Mathematical Society

American Mathematical Society