%0 Journal Article
%T Structures on the way from classical to quantum spaces and their tensor products
%J Advances in Operator Theory
%I Tusi Mathematical Research Group (TMRG)
%Z 2538-225X
%A Helemskii, Alexander
%D 2017
%\ 10/01/2017
%V 2
%N 4
%P 447-467
%! Structures on the way from classical to quantum spaces and their tensor products
%K proto-Lambert space
%K L-bounded operator
%K proto-Lambert tensor product
%K Lambert space
%K Lambert tensor product
%R 10.22034/aot.1706-1189
%X 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.
%U http://www.aot-math.org/article_48029_0d40409e1cfb1b74fe5c9c32cf76cdbe.pdf