# Riesz-like bases in rigged Hilbert spaces

Risultato della ricerca: Article

8 Citazioni (Scopus)

### Abstract

The notions of Bessel sequence, Riesz-Fischer sequence and Riesz basis are generalized to a rigged Hilbert space D[t] ⊂ H ⊂ D^×[t^×]. A Riesz-like basis, in particular, is obtained by considering a sequence {ξ_n} ⊂ D which is mapped by a one-to-one continuous operator T : D[t] → H[\| \cdot \|] into an orthonormal basis of the central Hilbert space H of the triplet. The operator T is, in general, an unbounded operator in H. If T has a bounded inverse then the rigged Hilbert space is shown to be equivalent to a triplet of Hilbert spaces.
Lingua originale English 243-265 23 ZEITSCHRIFT FUR ANALYSIS UND IHRE ANWENDUNGEN 35 Published - 2016

### All Science Journal Classification (ASJC) codes

• Analysis
• Applied Mathematics