Abstract
For a linear operatorS in a Hilbert space ℋ, the relationship between the following properties is investigated: (i)S is singular (= nowhere closable), (ii) the set kerS is dense in ℋ, and (iii)D(S)∩ℛ(S)={0}.
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Koshmanenko, V.D., ôta, S. On characteristic properties of singular operators. Ukr Math J 48, 1677–1687 (1996). https://doi.org/10.1007/BF02529489
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DOI: https://doi.org/10.1007/BF02529489