2008/08/16 by Gabriel Larotonda, Larotonda, Gabriel
Mathematics · #15A45 (Primary) 47A30 #47A63 #47B10 (Secondary) #Advanced Banach Space Theory #Advanced Operator Algebra Research #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Operator Algebras (math.OA) #math.FA #math.OA #msc:15A45 #msc:47A30 #msc:47A63 #msc:47B10
paper · pdf · doi:10.48550/arxiv.0808.2275
23 pages
arxiv created 2008/08/16 · openalex publication_date 2008/08/16 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we introduce a new technique for proving norm inequalities in operator ideals with an unitarily invariant norm. Among the well known inequalities which can be proved with this technique are the Löwner-Heinz inequality, inequalities relating various operator means and the Corach-Porta-Recht inequality. We prove two general inequalities and from them we derive several inequalities by specialization, many of them new. We also show how some inequalities, known to be valid for matrices or bounded operators, can be extended with this technique to normed ideals in C^*-algebras, in particular to the noncommutative Lp-spaces of a semi-finite von Neumann algebra.