2019/10/15 by А. Б. Александров, Aleksandrov, Aleksei, Vladimir Peller +1
Mathematics · #Advanced Operator Algebra Research #Classical Analysis and ODEs (math.CA) #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.1910.06891
openalex publication_date 2019/10/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study in this paper properties of Schur multipliers of Schatten von Neumann classes \boldsymbolSp. We prove that for p≤1, Schur multipliers of \boldsymbolSp are necessarily completely bounded. We also introduce for p≤1 a scale \mathscr Wp of tensor products of ℓ^∞ and prove that matrices in \mathscr Wp are Schur multipliers of \boldsymbolSp. We compare this sufficient condition with the sufficient condition of membership in the p-tensor product of ℓ^∞ spaces.