(BB) properties on Fréchet spaces

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In this paper we point out some relations concerning properties (BB)(n) and (BB)(n,s) related to the "Probleme des topologies" of Grothendieck and give a first example of a Frechet space with the (BB)(2) property but without the (BB)(3) property.
Ansemil, J.M., F. Blasco, and S. Ponte: On the “three-space problem" for spaces of polynomials. - Proceedings of the II International Workshop on Functional Analysis at Trier University, Trier Univ. 17, 1997, 189-195. Ansemil, J.M., and K. Floret: The symmetric tensor product of a direct sum of locally convex spaces. - Studia Math. 129, 1998, 285-295. Ansemil, J.M., and J. Taskinen: On a problem of topologies in infinite dimensional holomorphy. - Arch. Math. (Basel) 54, 1990, 61-64. Arias, A., and J.D. Farmer: On the structure of tensor products of lp -spaces. – Pacific J. Math. 175, 1996, 13-37. Bierstedt, K., and J. Bonet: Density conditions in Fréchet and (DF)-spaces. - Rev. Mat. Univ. Complut. Madrid 2, 1989, 59-75. Blasco, F.: Complementación, casinormabilidad y tonelación en espacios de polinomios. - Ph. D. Thesis, Universidad Complutense de Madrid, 1996. Blasco, F.: Complementation in spaces of symmetric tensor products and polynomials. - Studia Math. 123, 1997, 165-173. Bonet, J., and J.C. Díaz: The problem of topologies of Grothendieck and the class of Fréchet T-spaces. - Math. Nachr. 150, 1991, 109-118. Defant, A., and K. Floret: Tensor Norms and Operator Ideals. - North-Holland Math.Stud. 176, 1993. Defant, A., and M. Maestre: Property (BB) and holomorphic functions on Fréchet-Montel spaces. - Math. Proc. Cambridge Philos. Soc. 115, 1993, 305-313. Defant, A., and A. Peris: Maurey's extension theorem and Grothendieck's “problµeme des topologies". - J. London Math. Soc. (2) 58, 1998, 679-696. Díaz, J.C.: An example of a Fréchet space, non Montel, without infinite dimensional normable subspaces. - Proc. Amer. Math. Soc. 96, 1986, 721. Díaz, J.C., and G. Metafune: The problem of topologies of Grothendieck for quojections. - Results Math. 21, 1992, 299-311. Diestel, J., H. Jarchow, and A. Tonge: Absolutely Summing Operators. – Cambridge Stud. Adv. Math. 43, 1995. Dineen, S.: Complex Analysis in Locally Convex Spaces. - North-Holland Math. Stud. 57, 1981. Dineen, S.: Holomorphic functions on Fréchet-Montel spaces. - J. Math. Anal. Appl. 163, 1992, 581-587. Dineen, S.: Holomorphic functions and the (BB) property. - Math. Scand. 74, 1994, 215-236. Dineen, S.: Complex Analysis on Infinite Dimensional Spaces. - Springer-Verlag Monograph Series, 1999. Floret, K.: Natural norms on symmetric tensor products of normed spaces. - Proceedings of the II International Workshop on Functional Analysis at Trier University, Trier Univ., 17, 1997, 153-188. Galindo, P., D. García, and M. Maestre: The coincidence of 0 and ω for spaces of holomorphic functions on some Fréchet-Montel spaces. - Proc. Roy. Irish Acad. Sect. A 91, 1991, 137-143. Grothendieck, A.: Produits tensoriels topologiques et espaces nucleaires. - Mem. Amer. Math. Soc. 16, 1955. Metafune, G., and V.B. Moscatelli: On the space lp+ = ∩ q>p lq . - Math. Nachr. 147, 1990, 7-12. Oja, E.: Sur la réflexivité des produits tensoriels et les sous-spaces des produits tensoriels projectifs. - Math. Scand. 51, 1982, 75-288. Peris, A.: Quasinormable spaces and the problem of topologies of Grothendieck. - Ann. Acad. Sci. Fenn. Math. 19, 1994, 167-203. Taskinen, J.: Counterexamples to “Problµeme des Topologies" of Grothendieck. - Ann. Acad. Sci. Fenn. Math. Diss. 63, 1986. Taskinen, J.: The projective tensor product of Fréchet-Montel spaces. - Studia Math. 91, 1988, 17-30. Taskinen, J.: Examples of non-distinguished Fréchet spaces. - Ann. Acad. Sci. Fenn. Math. 14, 1989, 75-88. Zalduendo, I.: An estimate for multilinear forms on lp spaces. - Proc. Roy. Irish. Acad. Sect. A 93, 1993, 137-142.