Multi-normed spaces based on non-discrete measures and their tensor products

摘要

Lambert discovered a new type of structures situated, in a sense, between normed spaces and abstract operator spaces. His definition was based on the notion of amplifying a normed space by means of the spaces l(2)(n). Later, several mathematicians studied more general structures ('p-multi-normed spaces') introduced by means of the spaces l(p)(n), 1 = p = infinity. We pass from l(p) to L-p(X, mu) with an arbitrary measure. This becomes possible in the framework of the non-coordinate approach to the notion of amplification. In the case of a discrete counting measure, this approach is equivalent to the approach in the papers mentioned.