Structures on the Way from Classical to Quantum Spaces and Their Tensor Products
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چکیده
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 L1-spaces. At the same time the Lambert tensor product is nice for Hilbert spaces with the minimal Lambert norm.
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