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Linear and bilinear operators and their zero-sets

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Abstract

We study the extent to which several classical results relating linear or multilinear forms and their zero-sets can be generalised to linear or bilinear operators with values in \({\mathbb {R}}^n\). We find some analogues of the classical theorems, and also some restrictions.

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References

  1. Adams, J.F.: Vector fields on spheres. Ann. Math. 75(2), 603–632 (1962)

    Article  MathSciNet  Google Scholar 

  2. Adams, J.F., Lax, P.D., Phillips, R.S.: On matrices whose real linear combinations are non-singular. Proc. Am. Math. Soc. 16, 318–322 (1965)

    MathSciNet  MATH  Google Scholar 

  3. Adams, J.F., Lax, P.D., Phillips, R.S.: Correction to on matrices whose real linear combinations are nonsingular. Proc. Am. Math. Soc. 17, 945–947 (1966)

    MathSciNet  MATH  Google Scholar 

  4. Aron, R., Cardwell, A., García, D., Zalduendo, I.: A multilinear Phelps’ lemma. Proc. Am. Math. Soc. 135(8), 2549–2554 (2007)

    Article  MathSciNet  Google Scholar 

  5. Aron, R., Downey, L., Maestre, M.: Zero sets and linear dependence of multilinear forms. Note Mat. 25(1), 49–54 (2006)

    MathSciNet  MATH  Google Scholar 

  6. James, I.M.: Spaces associated with Stiefel manifolds. Proc. London Math. Soc. 9(3), 115–140 (1959)

    Article  MathSciNet  Google Scholar 

  7. Kato, T.: Perturbation Theory for Linear Operators. Die Grundlehren der mathematischen Wissenschaften, Band 132 Springer, New York (1966)

  8. Phelps, R.: A representation theorem for bounded convex sets. Proc. Am. Math. Soc. 11, 976–983 (1960)

    Article  MathSciNet  Google Scholar 

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Acknowledgements

The authors would like to thank Professor Manuel Maestre Vera and Professor Domingo García for their fruitful conversations during the preparation of this document.

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Authors and Affiliations

  1. Universidad Torcuato Di Tella, Av. Figueroa Alcorta 7350, C1428BCW, Buenos Aires, Argentina

    Damián Pinasco & Ignacio Zalduendo

  2. CONICET, Buenos Aires, Argentina

    Damián Pinasco & Ignacio Zalduendo

Authors
  1. Damián Pinasco
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  2. Ignacio Zalduendo
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Correspondence to Damián Pinasco.

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Supported partially by PIP 112 201301 00422 CO (CONICET - Argentina).

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Pinasco, D., Zalduendo, I. Linear and bilinear operators and their zero-sets. Rev Mat Complut 34, 131–149 (2021). https://doi.org/10.1007/s13163-020-00352-0

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  • DOI: https://doi.org/10.1007/s13163-020-00352-0

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