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Proceedings of the American Mathematical Society

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On the comparability of $ A^{1/2}$ and $ A^{\ast 1/2}$


Author: Alan McIntosh
Journal: Proc. Amer. Math. Soc. 32 (1972), 430-434
MSC: Primary 47.40
MathSciNet review: 0290169
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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}}$.


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DOI: https://doi.org/10.1090/S0002-9939-1972-0290169-7
Keywords: Regularly accretive operator, square root of an operator, Hilbert space, closed bilinear form
Article copyright: © Copyright 1972 American Mathematical Society