Abstract
An algebra of operators having the property of the title is constructed and it is used to give examples related to some recent invariant subspace results.
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References
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1980 Mathematics Subject Classification. Primary 47D05, 47D25; Secondary 46H10. Research supported in part by NSF and NSERC.
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Hadwin, D., Nordgren, E., Radjabalipour, M. et al. A nil algebra of bounded operators on Hilbert space with semisimple norm closure. Integr equ oper theory 9, 739–743 (1986). https://doi.org/10.1007/BF01195810
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DOI: https://doi.org/10.1007/BF01195810