Linear and bilinear operators and their zero-sets

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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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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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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Keywords

  • Zero-sets
  • Linear operators
  • Bilinear operators
  • Phelps’ Lemma

Mathematics Subject Classification

  • Primary 46B20
  • Secondary 47H60