標題: SUMS AND PRODUCTS OF CYCLIC OPERATORS
作者: WU, PY
交大名義發表
應用數學系
National Chiao Tung University
Department of Applied Mathematics
關鍵字: CYCLIC OPERATOR;MULTICYCLIC OPERATOR;TRIANGULAR OPERATOR
公開日期: 1-Dec-1994
摘要: 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* is finite-dimensional. More precisely, if dimker T* less than or equal to k (2 less than or equal to k < infinity), 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.
URI: http://dx.doi.org/10.2307/2161173
http://hdl.handle.net/11536/2226
ISSN: 0002-9939
DOI: 10.2307/2161173
期刊: PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
Volume: 122
Issue: 4
起始頁: 1053
結束頁: 1063
Appears in Collections:Articles


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