Fong, C. K.; Sourour, A. R. Sums and products of quasi-nilpotent operators. (English) Zbl 0598.47016 Proc. R. Soc. Edinb., Sect. A 99, 193-200 (1984). It is proved that a bounded operator on Hilbert space is the sum of two quasi-nilpotent operators if and only if it is not a non-zero scalar plus a compact operator. Necessary conditions and sufficient conditions for an operator to be the product of two quasi-nilpotent operators are given. Cited in 8 Documents MSC: 47A65 Structure theory of linear operators Keywords:sum of two quasi-nilpotent operators; not a non-zero scalar plus a compact operator; product of two quasi-nilpotent operators PDFBibTeX XMLCite \textit{C. K. Fong} and \textit{A. R. Sourour}, Proc. R. Soc. Edinb., Sect. A, Math. 99, 193--200 (1984; Zbl 0598.47016) Full Text: DOI References: [1] DOI: 10.1090/S0002-9939-1966-0203464-1 · doi:10.1090/S0002-9939-1966-0203464-1 [2] DOI: 10.1090/S0002-9939-1973-0374955-1 · doi:10.1090/S0002-9939-1973-0374955-1 [3] DOI: 10.2307/1970564 · Zbl 0131.12302 · doi:10.2307/1970564 [4] DOI: 10.1007/BF02771730 · Zbl 0232.47033 · doi:10.1007/BF02771730 [5] DOI: 10.1017/S0013091500016436 · Zbl 0412.47009 · doi:10.1017/S0013091500016436 [6] Shoda, Japan. J. Math. 13 pp 361– (1936) [7] DOI: 10.1307/mmj/1028999848 · Zbl 0156.38102 · doi:10.1307/mmj/1028999848 [8] Halmos, A Hilbert Space Problem Book (1967) [9] Fillmore, Acta Sci. Math. (Szeged) 33 pp 179– (1972) [10] Schatten, Norm ideals of completely continuous operators (1960) · Zbl 0090.09402 · doi:10.1007/978-3-642-87652-3 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.