He present work deals with estimations of the n-th linear polarization constant c(H) n of an n-dimensional real Hilbert space H. We provide some new lower bounds on the value of sup ∥y∥=1 |〈x 1,y〉 ... 〈x n,y〉|, where x 1, ... ,x n are unit vectors in H. In particular, the results improve an earlier estimate of Marcus. However, the intriguing conjecture c(H) n= n n/2 remains open.
- Gram matrices
- Linear polarization constants
- Polynomials over normed spaces
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