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Sums and products of cyclic operators

Author: Pei Yuan Wu
Journal: Proc. Amer. Math. Soc. 122 (1994), 1053-1063
MSC: Primary 47A05; Secondary 47A68
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 $ {T^ \ast }$ is finite-dimensional. More precisely, if dim ker $ {T^ \ast } \leq k(2 \leq k < \infty )$, then T is the product of at most $ k + 2$ 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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Keywords: Cyclic operator, multicyclic operator, triangular operator
Article copyright: © Copyright 1994 American Mathematical Society

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