The random paving property for uniformly bounded matrices

• Autorzy: Joel A. Tropp
• Języki publikacji: EN

Abstrakty

EN

This note presents a new proof of an important result due to Bourgain and Tzafriri that provides a partial solution to the Kadison-Singer problem. The result shows that every unit-norm matrix whose entries are relatively small in comparison with its dimension can be paved by a partition of constant size. That is, the coordinates can be partitioned into a constant number of blocks so that the restriction of the matrix to each block of coordinates has norm less than one half. The original proof of Bourgain and Tzafriri involves a long, delicate calculation. The new proof relies on the systematic use of symmetrization and (noncommutative) Khinchin inequalities to estimate the norms of some random matrices.

Kategorie tematyczne

• 46B09: Probabilistic methods in Banach space theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2008
• Tom: 185
• Numer: 1
• Strony: 67-82

Daty

wydano

2008

Twórcy

autor

Joel A. Tropp

• Applied & Computational Mathematics, MC 217-50, California Institute of Technology, 1200 E. California Blvd., Pasadena, CA 91125-5000, U.S.A.

Identyfikatory

DOI

10.4064/sm185-1-4