A Pythagorean inequality

Document Type

Article

Publication Date

1-1-1995

Abstract

Let (v1, v2, v3,. ) be a sequence of elements of a Hilbert space, and suppose that (one or both of) the inequalities hold for every finite sequence of scalars (ai). If an element v0 is adjoined to (vi), then the resulting set satisfies (one or both of) where, denoting the norm of vo by r and its distance from the closed linear span of the vi by δ,. © 1995 American Mathematical Society.

Publication Title

Proceedings of the American Mathematical Society

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