Abstract:Abstract. Let {vx, v2 , v$ , ... } be a sequence of elements of a Hilbert space, and suppose that (one or both of) the inequalities d2J2aj < \[52a¡v¡\\2 < D2 £] aj hold for every finite sequence of scalars {a,} . If an element v0 is adjoined to {v¡} , then the resulting set satisfies (one or both of) d2JA,af < Eai'vill2 ^ ^o ¿A,a2 » where, denoting the norm of vo by r and its distance from the closed linear span of the v¡ by ô , d2 = d2 and + Ur2-d2-yV2 + d2)2 -4d262\ D2 = D2 + X-(r2 -D2 + y/(r2 + D2)2 -^D2S2\… Show more
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