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

Document Type: Original Article

Author

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.

Keywords

### Histroty

• Receive Date: 20 June 2017
• Revise Date: 06 July 2017
• Accept Date: 06 July 2017