Publication: Tensor topologies on spaces of symmetric tensor products
Loading...
Full text at PDC
Publication Date
2006
Authors
Advisors (or tutors)
Editors
Journal Title
Journal ISSN
Volume Title
Publisher
Università del Salento
Citations
Exportar
Abstract
Here we show how, in the general context of locally convex spaces, it is possible to get an n-tensor topology (on spaces of n-tensor products) from an n-tensor topology on
spaces of symmetric n-tensors products. Indeed, given an n-tensor topology on the spaces of symmetric n-tensor products we construct an n-tensor topology on the spaces of all n-tensor products whose restriction to the symmetric ones gives the original topology. Moreover, we prove that when one starts with an n-tensor topology, restricts it to symmetric tensors and
then extends it, the original topology is obtained when it is symmetric, and we also obtain
some results on complementation with applications to spaces of polynomials. Part of these
results generalize to the context of locally convex spaces some Floret's results in [17] and [18].
Description
Dedicated to the memory of Klaus Floret (1941-2002)
UCM subjects
Unesco subjects
Keywords
Citation
R. Alencar: On re exivity and basis for P( mE), Proc. Roy. Irish. Acad. Sect. A, 85 n. 2, 131{138, 1985.
J. M. Ansemil, F. Blasco, S. Ponte: (BB) properties on Fréchet spaces, Ann. Acad. Sci. Fenn. Math. 25, 370{316, 2000.
J. M. Ansemil, K. Floret: The symmetric tensor product of a direct sum of locally convex spaces, Studia Math., 129, n. 3, 285{295, 1998.
J. M. Ansemil, J. Taskinen: On a problem of topologies in infinite dimensional holomorhpy, Arch. Math. (Basel) 54, 61{64, 1990.
R. Aron, M. Schottenloher: Compact Holomorphic Mappings on Banach Spaces and the Approximation Property, J. Funct. Anal. 21, 7{30, 1976.
F. Blasco: Complementation in spaces of symmetric tensor products and polynomials, Studia Math. 123, n. 2, 165{173, 1997.
J. Bonet, A. Peris: On the Injective Tensor Product of Quasinormable Spaces. Results in Maths. 20, 431{443, 1991.
C. Boyd: Holomorphic Functions and the BB-property on Product Spaces, J. Korean Math. Soc. 41, n. 1, 39{50, 2004.
D. Carando, I. Zalduendo: A Hahn-Banach theorem for integral polynomials, Proc. Amer. Math. Soc. 127, n. 1, 241{250, 1999.
A. Defant, K. Floret: Tensor Norms and Operator Ideals, North-Holland Math. Stud. 176, 1993.
A. Defant, J. C. D az, D. Garc a, M. Maestre: Unconditional basis and Gordon Lewis constants for spaces of polynomials, J. Funct. Anal. 181, 119{145, 2001.
A. Defant, M. Maestre: Property (BB) and holomorphic functions on Fréchet-Montel spaces. Math. Proc. Cambridge Philos. Soc., 115, 305{313, 1993.
S. Dineen: Holomorphy types on a Banach space, Studia Math. 39, 241{288, 1971.
S. Dineen: Complex Analysis on Infinite Dimensional Spaces, Springer Monographs in Math., Springer, 1999.
K. Floret: Some aspects of the theory of locally convex inductive limits, Functional Analysis: Surveys and Recent Results II, K.D. Bierstedt and B. Fuchssteiner Eds. NorthHolland, 205{237, 1980.
K. Floret: Tensor topologies and equicontinuity, Note Mat. 5, 37{49, 1985.
K. Floret: Natural norms on symmetric tensor products of normed spaces, Note Mat. 17, pp. 153-188, 1997.
K. Floret: The extension theorem for norms on symmetric tensor products of normed spaces, Recent Progress in Functional Analysis. K.D. Bierstedt et al. Eds. North Holland Math. Studies 189, 225{237, 2001.
A. Grothendieck: Produits tensoriels et espaces nucl eaires, Mem. Amer. Math. Soc. 16, 1955.
H. Jarchow: Locally Convex Spaces, B.G. Teubner, Stuttgart, 1981.
G. Kothe � : Topological Vector Spaces II. Springer-Verlag, Berlin, 1979.
R. Ryan: Applications of topological tensor products to infinite dimensional holomorphy. Ph. D. thesis, Trinity College Dublin, 1980.
R. Ryan: Introduction to Tensor Products of Banach Spaces, Springer Monographs in Math., Springer, 2002.