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 |
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pagine (da-a) | 243-265 |
Numero di pagine | 23 |
Rivista | ZEITSCHRIFT FUR ANALYSIS UND IHRE ANWENDUNGEN |
Volume | 35 |
Stato di pubblicazione | Published - 2016 |
All Science Journal Classification (ASJC) codes
- ???subjectarea.asjc.2600.2603???
- ???subjectarea.asjc.2600.2604???