RT Journal Article
T1 The real plank problem and some applications.
A1 Muñoz-Fernández, Gustavo A.
A1 Sarantopoulos, Y
A1 Seoane-Sepúlveda, Juan B.
AB K. Ball has proved the "complex plank problem": if (x(k))(k=1)(n) is a sequence of norm I vectors in a complex Hilbert space (H, (., .)), then there exists a unit vector x for which |< x,x(k)>| >= 1/root n, k = 1,...,n. In general, this result is not true on real Hilbert spaces. However, in special cases we prove that the same result holds true. In general, for some unit vector x we have derived the estimate |< x,x(k)>| >= max{root lambda(1)/n, 1/root lambda(n)n}, where lambda(1) is the smallest and lambda(n) is the largest eigenvalue of the Hermitian matrix A = [(x(j), x(k))], j, k = 1,...,n. We have also improved known estimates for the norms of homogeneous polynomials which are products of linear forms on real Hilbert spaces.
PB American Mathematical Society
SN 0002-9939
YR 2010
FD 2010
LK https://hdl.handle.net/20.500.14352/43652
UL https://hdl.handle.net/20.500.14352/43652
LA eng
NO C. Caratheodory
DS Docta Complutense
RD 7 abr 2025