Sums and products of cyclic operators

Author:
Pei Yuan Wu

Journal:
Proc. Amer. Math. Soc. **122** (1994), 1053-1063

MSC:
Primary 47A05; Secondary 47A68

DOI:
https://doi.org/10.1090/S0002-9939-1994-1203995-9

MathSciNet review:
1203995

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Abstract: It is proved that every bounded linear operator on a complex separable Hilbert space is the sum of two cyclic operators. For the product, we show that an operator *T* is the product of finitely many cyclic operators if and only if the kernel of is finite-dimensional. More precisely, if dim ker , then *T* is the product of at most cyclic operators. We conjecture that in this case at most *k* cyclic operators would suffice and verify this for some special classes of operators.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1994-1203995-9

Keywords:
Cyclic operator,
multicyclic operator,
triangular operator

Article copyright:
© Copyright 1994
American Mathematical Society