Arkiv för Matematik

  • Ark. Mat.
  • Volume 43, Number 1 (2005), 167-180.

Tensor products of direct sums

Bogdan C. Grecu and Raymond A. Ryan

Full-text: Open access

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.

Article information

Source
Ark. Mat. Volume 43, Number 1 (2005), 167-180.

Dates
Received: 16 June 2003
First available in Project Euclid: 31 January 2017

Permanent link to this document
https://projecteuclid.org/euclid.afm/1485898875

Digital Object Identifier
doi:10.1007/BF02383617

Mathematical Reviews number (MathSciNet)
MR2134705

Zentralblatt MATH identifier
1096.46037

Rights
2005 © Institut Mittag-Leffler

Citation

Grecu, Bogdan C.; Ryan, Raymond A. Tensor products of direct sums. Ark. Mat. 43 (2005), no. 1, 167--180. doi:10.1007/BF02383617. https://projecteuclid.org/euclid.afm/1485898875


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References

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  • Defant, A. and Floret, K., Tensor Norms and Operator Ideals, North-Holland, Amsterdam, 1993.
  • Díaz, J. C. and Dineen, 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. and Harris, J., Representation Theory. A First Course, Graduate Texts in Mathematics 129, Springer-Verlag, New York, 1991.
  • Ryan, R. A., Introduction to Tensor Products of Banach Spaces, Springer Monographs in Mathematics, Springer-Verlag, London, 2002.