A Marcinkiewicz theory for Schur-Multipliers on Schatten-von Neumann Classes

Tao Mei (Baylor University)

Thursday 28th July 16:00-17:00 Maths 311B

Abstract

The Schur product of two n by n matrices is a pointwise product. More precisely, the Schur product of $m= (m_{ij})$ and $A=(a_{ij})$ is the matrix $(m_{ij}a_{ij})$. Let us fix the matrix m and view the Schur product of matrices with m as a map on the matrix algebra, which we call a Schur multiplier. The boundedness of Schur multipliers (with more general indices)  naturally connects to the approximation property of group von Neumann algebras as shown in the work of Haagerup, Lafforgue/de la Salle,  Parcet/de la Salle/Ricard, and Parcet etc.

 

In this talk, I plan to introduce an analogue of Marcinkiewicz-multiplier theory for Schur multipliers on Schatten-p classes. The talk will be based on a recent work with ChianYeong Chuah and Zhenchuan Liu.

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