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arXiv · 1706.00623

Structures on the way from classical to quantum spaces and their tensor products

A. Ya. Helemskii
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Abstract

We study tensor products of two structures situated, in a sense, between normed spaces and (abstract) operator spaces. We call them Lambert and proto-Lambert spaces and pay more attention to the latter ones. The considered two tensor products lead to essentially different norms in the respective spaces. Moreover, the proto-Lambert tensor product is especially nice for spaces with the maximal proto-Lambert norm and in particular, for $L_1$-spaces. At the same time the Lambert tensor product is nice for Hilbert spaces with the minimal Lambert norm.

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A. Ya. Helemskii. 2017-06-02. Structures on the way from classical to quantum spaces and their tensor products. https://arxiv.org/abs/1706.00623

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