Tensor splitting properties of n-inverse pairs of operators

Stepan Paul; Caixing Gu

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arXiv · 1511.07505

Tensor splitting properties of n-inverse pairs of operators

Stepan Paul·Caixing Gu

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Abstract

In this paper we study n-inverse pairs of operators on the tensor product of Banach spaces. In particular we show that an n-inverse pair of elementary tensors of operators on the tensor product of two Banach spaces can arise only from l- and m-inverse pairs of operators on the individual spaces. This gives a converse to a result of Duggal and Müller, and proves a conjecture of the second named author. Our proof uses techniques from algebraic geometry, which generalize to other relations among operators in a tensor product. We apply this theory to obtain results for n-symmetries in a tensor product as well.

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BibTeX RIS

Stepan Paul, Caixing Gu. 2015-11-23. Tensor splitting properties of n-inverse pairs of operators. https://arxiv.org/abs/1511.07505

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