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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