On the comparability of 𝐴^{1/2} and 𝐴^{∗1/2}

McIntosh, Alan

doi:10.1090/S0002-9939-1972-0290169-7

On the comparability of $A^{1/2}$ and $A^{\ast 1/2}$
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Proc. Amer. Math. Soc. 32 (1972), 430-434 Request permission

Abstract:

There exists a regularly accretive operator A in a Hilbert space H such that ${A^{1/2}}$ and ${A^{ \ast 1/2}}$ have different domains. Consequently, the domain of the closed bilinear form corresponding to A is different from the domain of ${A^{1/2}}$.

References

Tosio Kato, Fractional powers of dissipative operators, J. Math. Soc. Japan 13 (1961), 246–274. MR 138005, DOI 10.2969/jmsj/01330246
Tosio Kato, Fractional powers of dissipative operators. II, J. Math. Soc. Japan 14 (1962), 242–248. MR 151868, DOI 10.2969/jmsj/01420242
Tosio Kato, Perturbation theory for linear operators, Die Grundlehren der mathematischen Wissenschaften, Band 132, Springer-Verlag New York, Inc., New York, 1966. MR 0203473
Alan McIntosh, Counterexample to a question on commutators, Proc. Amer. Math. Soc. 29 (1971), 337–340. MR 276798, DOI 10.1090/S0002-9939-1971-0276798-4
J.-L. Lions, Espaces d’interpolation et domaines de puissances fractionnaires d’opérateurs, J. Math. Soc. Japan 14 (1962), 233–241 (French). MR 152878, DOI 10.2969/jmsj/01420233
Alan G. R. McIntosh, Bilinear forms in Hilbert space, J. Math. Mech. 19 (1969/1970), 1027–1045. MR 0261392