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The symmetric tensor product of a direct sum of locally convex spaces

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dc.contributor.authorAnsemil, José María M.
dc.contributor.authorFloret, Klaus
dc.date.accessioned2023-06-20T17:00:38Z
dc.date.available2023-06-20T17:00:38Z
dc.date.issued1988
dc.description.abstractAn explicit representation of the n-fold symmetric tensor product (equipped with a natural topology tau such as the projective, injective or inductive one) of the finite direct sum of locally convex spaces is presented. The formula for circle times(tau,delta)(n)(F-1 circle plus F-2) gives a direct proof of a recent result of Diaz and Dineen land generalizes it to other topologies tau) that the n-fold projective symmetric and the n-fold projective "full" tensor product of a Iocally convex space fare isomorphic if E is isomorphic to its square E-2.
dc.description.departmentDepto. de Análisis Matemático y Matemática Aplicada
dc.description.facultyFac. de Ciencias Matemáticas
dc.description.refereedTRUE
dc.description.sponsorshipUCM
dc.description.statuspub
dc.eprint.idhttps://eprints.ucm.es/id/eprint/16794
dc.identifier.citationR. Alencar and K. Floret, Weak-strong contínuity of multilinear mappings and the Pelezyński-Pitt-theorem, J. Math. Anal. Appl. 206 (1997), 532-546. A. Arias and J. Farmer, On the structure of tensor products of lp-spaces, Pacific J. Math. 175 (1996), 13-37. F. Blasco, Complementación, casinorrnabilidad y tonelación en espacios de polinomios , doct. thesis, Univ. Compl. Madrid, 1996. F. Blasco, Complementation in spaces of symmetric tensor products and polynomials, Studia Math. 123 (1997) 165-173. J. Bonet and A. Peris, On the injective tensor product of quasinormable spaces, Results in Math. 20 (1991), 431-443. J A. Defan t and K. Floret, Tensor Norms and Operator Ideals, North-Holland Math. Stud. 176, North-Holland, 1993. A. Defant and M. Maestre, Property (BB) and holomorphie junetions on Fréchet-Montel spaces, Math. Proc. Cambridge Philos. Soc. 115 (1993), 305-313. J. C. Díaz and S. Dineen, Polynomials on stable spaces, Ark. Mat. to appear. S. Dineen, Complex Analysis on Infinite Dimensional Spaces, in preparation. K. F loret, Some aspeets of the theory locally convex inductive limits, in, Functional Analysis: Surveys and Recent Results II, K, D. Bierstedt and B. Fuchssteiner (ed,.), North-Holland, 1980,205-237. K. F loret, Tensor topologies and equicontinuity, Note Mat. 5 (1985), 37--49. W. T. Gowers, A solution to the Schroeder-Bernstein problem for Banach spaces, Bull. London Math. Soc. 28 (1996), 297-304. W. Greub, Multilinear Algebra, Universitext, Springer, 1978. A, Grothendieck, Produits tensoriels et espaces nucléaires, Mem. Amer. Math. Soc. 16 (1955. H. Jarchow, Locally Conv ex Spaces, Teubner, 1981. R. Ryan, Applieation of topological tensor products to infinite dimensional holomorphy, doct. thesis, Trinity Coll. Dublin, 1980. L. Schwartz, Théorie des distributions à values vectorielles. I et II, Ann. Inst. Fourier (Grenoble) 7 (1957), 1-141, and 8 (1958), 1-209.
dc.identifier.issn0039-3223
dc.identifier.officialurlhttp://webmail.impan.gov.pl/sm/
dc.identifier.relatedurlhttp://webmail.impan.gov.pl/
dc.identifier.urihttps://hdl.handle.net/20.500.14352/57618
dc.issue.number3
dc.journal.titleStudia Mathematica
dc.language.isoeng
dc.page.final295
dc.page.initial285
dc.publisherPolish Acad Sciencies Inst Mathematics
dc.relation.projectIDPB295/95-6140
dc.rights.accessRightsopen access
dc.subject.cdu515.1
dc.subject.keywordsymmetric tensor products
dc.subject.keywordcontinuous n-homogeneous polynomials
dc.subject.keywordtensor topologies
dc.subject.ucmTopología
dc.subject.unesco1210 Topología
dc.titleThe symmetric tensor product of a direct sum of locally convex spaces
dc.typejournal article
dc.volume.number129
dspace.entity.typePublication
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