Optimal constants in non-commutative Hölder inequality for quasi-norms

Sukochev, F.; Zanin, D.

doi:10.1090/proc/15442

Optimal constants in non-commutative Hölder inequality for quasi-norms
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Proc. Amer. Math. Soc. 149 (2021), 3813-3817 Request permission

Abstract:

We resolve an open problem due to B. Simon [Trace ideals and their applications, Cambridge University Press, Cambridge–New York, 1979; Trace ideals and their applications, American Mathematical Society, Providence, RI, 2005] concerning optimal constants in Hölder inequality for certain quasi-normed principal ideals of importance in Mathematical Physics and Noncommutative Geometry.

References

Alain Connes, Noncommutative geometry, Academic Press, Inc., San Diego, CA, 1994. MR 1303779
Ken Dykema and Anna Skripka, Hölder’s inequality for roots of symmetric operator spaces, Studia Math. 228 (2015), no. 1, 47–54. MR 3416953, DOI 10.4064/sm228-1-5
Daniele Guido and Tommaso Isola, Dimensions and singular traces for spectral triples, with applications to fractals, J. Funct. Anal. 203 (2003), no. 2, 362–400. MR 2003353, DOI 10.1016/S0022-1236(03)00230-1
Steven Lord, Fedor Sukochev, and Dmitriy Zanin, Singular traces, De Gruyter Studies in Mathematics, vol. 46, De Gruyter, Berlin, 2013. Theory and applications. MR 3099777
Richard O’Neil, Convolution operators and $L(p,\,q)$ spaces, Duke Math. J. 30 (1963), 129–142. MR 146673
Barry Simon, Trace ideals and their applications, London Mathematical Society Lecture Note Series, vol. 35, Cambridge University Press, Cambridge-New York, 1979. MR 541149
Barry Simon, Trace ideals and their applications, 2nd ed., Mathematical Surveys and Monographs, vol. 120, American Mathematical Society, Providence, RI, 2005. MR 2154153, DOI 10.1090/surv/120
F. Sukochev, Hölder inequality for symmetric operator spaces and trace property of K-cycles, Bull. Lond. Math. Soc. 48 (2016), no. 4, 637–647. MR 3532139, DOI 10.1112/blms/bdw022