Schmidt Representation of Bilinear Operators on Hilbert Spaces

Eduardo Brandani da Silva; Dicesar Lass Fernandez; Marcus Vinícius de Andrade Neves

Schmidt Representation of Bilinear Operators on Hilbert Spaces

Functional Analysis 2021-08-09 v1

Authors: Eduardo Brandani da Silva , Dicesar Lass Fernandez , Marcus Vinícius de Andrade Neves

Abstract

Current work defines Schmidt representation of a bilinear operator $T: H_1 \times H_2 \rightarrow K$ , where $H_1, H_2$ and $K$ are separable Hilbert spaces. Introducing the concept of singular value and ordered singular value, we prove that if $T$ is compact, and its singular values are ordered, then $T$ has a Schmidt representation on real Hilbert spaces. We prove that the hypothesis of existence of ordered singular values is fundamental.

Keywords

operator theory on hilbert spaces operator theory group representations

Cite

@article{arxiv.2108.02869,
  title  = {Schmidt Representation of Bilinear Operators on Hilbert Spaces},
  author = {Eduardo Brandani da Silva and Dicesar Lass Fernandez and Marcus Vinícius de Andrade Neves},
  journal= {arXiv preprint arXiv:2108.02869},
  year   = {2021}
}

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27 pages

Schmidt Representation of Bilinear Operators on Hilbert Spaces

Abstract

Keywords

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