Title: Schur/Hadamard Multipliers on Large Matrices

 

Abstract: The boundedness of Schur/Hadamard Products plays an important role in engineering and data science. In particular, the storage of information in large data is closely related to the study of the boundedness of the Schatten-p norm of matrices in non-commutative harmonic analysis. In this talk, we provide a Marcinkiewicz type multiplier theory for the Schur multipliers on the Schatten p-classes. This generalizes a previous result of Bourgain for Toeplitz type Schur multipliers and complements a recent result by Conde-Alonso, Gonzalez-Perez, Parcet and Tablate. As a corollary, we obtain a new unconditional decomposition for the Schatten p-classes for p>1. Similar results can also be extended to the case of R^{d} and Z^{d}, where d≥2.