Fractional powers on noncommutative L p for p < 1

Fractional powers on noncommutative L p for p < 1

We prove that the homogeneous functional calculus associated to x → |x| θ or x → sgn (x)|x| θ for 0 < θ < 1 is θ-Hölder on selfadjoint elements of noncommutative Lp-spaces for 0 < p ∞ with values in L p/θ. This extends an inequality of Birman, Koplienko and Solomjak also obtained by Ando....

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Veröffentlicht in:Advances in mathematics (New York. 1965) 2018-07, Vol.333, p.194-211
1. Verfasser: Ricard, Éric
Format: Artikel
Sprache:eng
Schlagworte:
Functional Analysis
Mathematics
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Zusammenfassung:We prove that the homogeneous functional calculus associated to x → |x| θ or x → sgn (x)|x| θ for 0 < θ < 1 is θ-Hölder on selfadjoint elements of noncommutative Lp-spaces for 0 < p ∞ with values in L p/θ. This extends an inequality of Birman, Koplienko and Solomjak also obtained by Ando.
ISSN:0001-8708
1090-2082
DOI:10.1016/j.aim.2018.05.024