Riesz-like bases in rigged Hilbert spaces

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16 Citations (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.
Original languageEnglish
Pages (from-to)243-265
Number of pages23
JournalZEITSCHRIFT FUR ANALYSIS UND IHRE ANWENDUNGEN
Volume35
Publication statusPublished - 2016

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

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