The operator factorization problems. (English) Zbl 0673.47018
Which bounded linear operator on a Hilbert space can be factored as the product of finitely many normal operators? What is the answer if “normal operators” is replaced by “involutions”, “partial isometries” or other classes of familiar operators? The author surveys various results concerning these operator factorization problems. This paper can serve as a convenient reference so that to enhance people’s interest in this area of research. This has 6 sections, 69 theorems and 71 references.
Reviewer: T.Nakazi
MSC:
| 47A68 | Factorization theory (including Wiener-Hopf and spectral factorizations) of linear operators |
| 47B15 | Hermitian and normal operators (spectral measures, functional calculus, etc.) |
Keywords:
Which bounded linear operator on a Hilbert space can be factored; as the product of finitely many normal operators?; involutions; partial isometries; operator factorization problems; Which bounded linear operator on a Hilbert space can be factored as the product of finitely many normal operators?References:
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