The role of algebraic structure in the invariant subspace theory

The role of algebraic structure in the invariant subspace theory

Following a recent work of authors [1], we establish the algebraic analogs of three major decomposition theorems of Nagy-Foias-Langer, Halmos-Wallen and Fishel in Baer ⁎-rings. This approach not only provides purely algebraic and shorter proofs of these decomposition theorems, but also suggests the...

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Veröffentlicht in:Linear algebra and its applications 2019-12, Vol.583, p.102-118
Hauptverfasser: Bagheri-Bardi, G.A., Elyaspour, A., Esslamzadeh, G.H.
Format: Artikel
Sprache:eng
Schlagworte:
Algebra
Baer ⁎-ring
Compression
Contraction
Decomposition
Invariants
Linear algebra
Partial isometry
Power partial isometry
Rings (mathematics)
Shift
Theorems
Truncated shift
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Beschreibung
Zusammenfassung:Following a recent work of authors [1], we establish the algebraic analogs of three major decomposition theorems of Nagy-Foias-Langer, Halmos-Wallen and Fishel in Baer ⁎-rings. This approach not only provides purely algebraic and shorter proofs of these decomposition theorems, but also suggests the possibility of eliminating the role of analytic structure in results related to the invariant subspace theory.
ISSN:0024-3795
1873-1856
DOI:10.1016/j.laa.2019.08.022