Banach Gelfand triples are an important subset from the modulation spaces.
Starting from the Segal algbra S_0(Rd) and its dual one can use the
notion of (unitary) Banach Gelfand triple isomorphism to describe e.g.
the Fourier transform, or the mapping between operator kernels
and their Kohn-Nirenberg symbol or their spreading distribution
in a technically not so difficult way, building on standard functional
analytic concepts only.