Abstract
A similar formula to the one established by Ansemil and Floret for symmetric tensor products of direct sums is proved for alternating and Jacobian tensor products. It is then applied to stable spaces where a number of isomorphisms between spaces of tensors or multilinear forms are unveiled. A connection between these problems and irreducible group representations is made.
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References
Ansemil, J. M. andFloret, K., The symmetric tensor product of a direct sum of locally convex spaces,Studia Math. 129 (1998), 285–295.
Defant, A. andFloret, K.,Tensor Norms and Operator Ideals, North-Holland, Amsterdam, 1993.
Díaz, J. C. andDineen, S., Polynomials on stable spaces,Ark. Mat. 36 (1998), 87–96.
Dineen, S.,Complex Analysis on Infinite Dimensional Spaces, Springer-Verlag, London, 1999.
Fulton, W. andHarris, J.,Representation Theory. A First Course, Graduate Texts in Mathematics129, Springer-Verlag, New York, 1991.
Ryan, R. A.,Introduction to Tensor Products of Banach Spaces, Springer Monographs in Mathematics, Springer-Verlag, London, 2002.
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Grecu, B.C., Ryan, R.A. Tensor products of direct sums. Ark. Mat. 43, 167–180 (2005). https://doi.org/10.1007/BF02383617
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DOI: https://doi.org/10.1007/BF02383617