Abstract
Various characterizations of unbounded closed densely defined operators commuting with the spectral measures of their moduli are established. In particular, Kaufman’s definition of an unbounded quasinormal operator is shown to coincide with that given by the third-named author and Szafraniec. Examples demonstrating the sharpness of results are constructed.
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Research of the first and the third authors was supported by the MNiSzW (Ministry of Science and Higher Education) Grant NN201 546438 (2010-2013). Research of the second author was supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIP) (No. 2009-0083521).
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Jabłoński, Z.J., Jung, I.B. & Stochel, J. Unbounded Quasinormal Operators Revisited. Integr. Equ. Oper. Theory 79, 135–149 (2014). https://doi.org/10.1007/s00020-014-2133-1
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DOI: https://doi.org/10.1007/s00020-014-2133-1