The notions of Bessel sequence, Riesz-Fischer sequence and Riesz basis are generalized to a rigged Hilbert space . A Riesz-like basis, in particular, is obtained by considering a sequence which is mapped by a one-to-one continuous operator into an orthonormal basis of the central Hilbert space of the triplet. The operator is, in general, an unbounded operator in . If has a bounded inverse then the rigged Hilbert space is shown to be equivalent to a triplet of Hilbert spaces.
Cite this article
Giorgia Bellomonte, Camillo Trapani, Riesz-Like Bases in Rigged Hilbert Spaces. Z. Anal. Anwend. 35 (2016), no. 3, pp. 243–265DOI 10.4171/ZAA/1564