1. * (a) Prove the Schwarz inequality ||a|| ||B|| | (a|)|. Hint: use the fact...

 

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1. * (a) Prove the Schwarz inequality ||a|| ||B|| ≥ | (a|ß)|. Hint: use the fact that ||a + cß|| ≥ 0 for any c E C. (b) Prove that the equality holds only if |B) = dla), with c E C. (c) Prove the triangular inequalities ||||||||||≤||a + B|| ≤ ||a|| + || B||. (d) Consider a) and 3) in a discrete Hilbert space. Prove the Schwarz inequality by considering the expan of a) and 3) in a basis {01), 2),...}. 1. * (a) Prove the Schwarz inequality ||a|| ||B|| ≥ | (a|ß)|. Hint: use the fact that ||a + cß|| ≥ 0 for any c E C. (b) Prove that the equality holds only if |B) = dla), with c E C. (c) Prove the triangular inequalities ||||||||||≤||a + B|| ≤ ||a|| + || B||. (d) Consider a) and 3) in a discrete Hilbert space. Prove the Schwarz inequality by considering the expan of a) and 3) in a basis {01), 2),...}.

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1 Schwarz Inequality B 4B Let 2 be not Linearly dependent ie a By independent then ac 0 for all CEC ... View the full answer