Sánchez Pérez, E. A. Vector measure orthonormal functions and best approximation for the 4-norm. (English) Zbl 1036.46031 Arch. Math. 80, No. 2, 177-190 (2003). For a vector measure \(\lambda\) with values in a Hilbert space, the notions of \(\lambda\)-orthogonality for pairs of \(\lambda\)-integrable functions and \(\lambda\)-orthonormality for sequences of functions are defined. Then, it is proved that, under certain conditions, such a sequence generates a function space isometric to the sequence space \(\ell_4\) when endowed with the 4-norm. Then there follows a discussion of the relationship between \(\lambda\)-orthogonal functions and best approximation for the 4-norm. Reviewer: Srinivasa Swaminathan (Halifax) Cited in 5 Documents MSC: 46G10 Vector-valued measures and integration 46B45 Banach sequence spaces Keywords:Hilbert space valued vector measures; sequence spaces PDFBibTeX XMLCite \textit{E. A. Sánchez Pérez}, Arch. Math. 80, No. 2, 177--190 (2003; Zbl 1036.46031) Full Text: DOI