2026-06-29T07:50:47Zhttps://docta.ucm.es/rest/oai/request

oai:docta.ucm.es:20.500.14352/436522025-05-23T17:53:37Zcom_20.500.14352_14col_20.500.14352_15

The real plank problem and some applications. Muñoz-Fernández, Gustavo A. Sarantopoulos, Yannis Seoane Sepúlveda, Juan Benigno 517.98 Plank problems Polarization constants Product of linear functionals Análisis funcional y teoría de operadores 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. C. Caratheodory Depto. de Análisis Matemático y Matemática Aplicada Fac. de Ciencias Matemáticas Instituto de Matemática Interdisciplinar (IMI) TRUE pub 2023-06-20T03:30:44Z 2023-06-20T03:30:44Z 2010 journal article https://hdl.handle.net/20.500.14352/43652 0002-9939 10.1090/S0002-9939-10-10295-0 eng MTM2006-03531. No. 65/1602. MTM2006-03531. restricted access application/pdf American Mathematical Society