Let X be an inner product space over C and x, y = X are such that || x + y || = || x-y ||, then show that xly.

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Q: If X is an inner product space and A = {0} , then A- = {0}O AO

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Q: Thm. Let v be an inner product Space then and HyE V жує ||≤|12||· 1191/ further equility is hold iff…

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Q: Thm. Let v be an V be an inner product Space V and then жує | 13 11211. 11111 further equility is…

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Q: 5. Let V be an inner product space over C. Show that for any v, w e V (v, (v, w)w) = | (v, w) |² and…

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Q: Let V be an inner product space and u, v € V. Prove the following identity: ||u + v||² − ||u − v||²…

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Q: Let X & Y be normed spaces & x # 204. Then BL (X₂Y) is a Banach space in the operator norm if and…

A: Here BL(X,Y) (or, B(X,Y)), is the space of bounded linear operators from X to Y. First ,we show that…

Q: b) Let X be an inner product space and x, y e x.Prove that xly if and only if kx + y = |lk | + |y*k…

A: Given that X be an inner product space and x,y∈X Let, x⊥y. The objective is to prove that…

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Q: Let V be an inner product space. Show that ||cu|| |c| ||u|| for any vector u and any scalar c.

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Q: 1. Let V be an inner product space. Suppose f,g E V such that f -gg (a) Prove that 1I2 = |lf- gll2 +…

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Q: Let V is an inner product space. Prove, Va, y EV ||x+y||² + ||x − y||² = 2||x||² + 2||y||* . How…

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Q: is an Let V(F) be an inner product space. If 0 + o e V then prove that orthonormal set.

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Q: Let V be a finite-dimensional inner product space over F. (a) Prove that the trace of every positive…

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A: Theorem: Proof: