A+ CATEGORY SCIENTIFIC UNIT

Grothendieck’s inequality in the noncommutative Schwartz space

Volume 234 / 2016

Rupert H. Levene, Krzysztof Piszczek Studia Mathematica 234 (2016), 185-194 MSC: Primary 47A30, 47A07, 47L10; Secondary 47A63. DOI: 10.4064/sm8552-6-2016 Published online: 23 August 2016

Abstract

In the spirit of Grothendieck’s famous inequality from the theory of Banach spaces, we study a sequence of inequalities for the noncommutative Schwartz space, a Fréchet algebra of smooth operators. These hold in nonoptimal form by a simple nuclearity argument. We obtain optimal versions and reformulate the inequalities in several different ways.

Authors

  • Rupert H. LeveneSchool of Mathematics and Statistics
    University College Dublin
    Belfield, Dublin 4, Ireland
    e-mail
  • Krzysztof PiszczekFaculty of Mathematics and Computer Science
    Adam Mickiewicz University in Poznań
    Umultowska 87
    61-614 Poznań, Poland
    e-mail

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