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arXiv · 2108.02869

Schmidt Representation of Bilinear Operators on Hilbert Spaces

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

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Eduardo Brandani da Silva, Dicesar Lass Fernandez, Marcus Vinícius de Andrade Neves. 2021-08-05. Schmidt Representation of Bilinear Operators on Hilbert Spaces. https://arxiv.org/abs/2108.02869

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