Geodesic
Bounds for Fractional Powers of Operators in a Hilbert Space and Constants in Moment Inequalities
Fractional calculus and applied analysis, Tome 12 (2009) no. 1, pp. 57-69.

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We derive bounds for the norms of the fractional powers of operators with compact Hermitian components, and operators having compact inverses in a separable Hilbert space. Moreover, for these operators, as well as for dissipative operators, the constants in the moment inequalities are established.
Keywords: Linear Operator, Fractional Powers, Moment Inequality, Dissipative Operator, Compact Hermitian Component, Compact Inverse, 47A56, 47A57, 47A63 
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     author = {I. Gil{\textquoteright}, Michael},
     title = {Bounds for {Fractional} {Powers} of {Operators} in a {Hilbert} {Space} and {Constants} in {Moment} {Inequalities}},
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     year = {2009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/FCAA_2009_12_1_a4/}
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I. Gil’, Michael. Bounds for Fractional Powers of Operators in a Hilbert Space and Constants in Moment Inequalities. Fractional calculus and applied analysis, Tome 12 (2009) no. 1, pp. 57-69. http://geodesic.mathdoc.fr/item/FCAA_2009_12_1_a4/