Extreme points and optimal measures. (English) Zbl 1217.15029
Summary: We provide a new and more efficient proof of our earlier result that every \(2\times 2\) Toeplitz matrix \(M\) has a representing measure \(\mu \) that is optimal in the sense that \(\| \mu \| =\| M\| _S\), the norm of \(M\) as a Schur multiplier. This result is seen to follow from some elementary observations about extreme points in the unit ball of trigonometric trinomials. We also discuss the complete characterization of such extreme points.
MSC:
| 15A60 | Norms of matrices, numerical range, applications of functional analysis to matrix theory |
| 15B05 | Toeplitz, Cauchy, and related matrices |
| 15A18 | Eigenvalues, singular values, and eigenvectors |
| 15A45 | Miscellaneous inequalities involving matrices |
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