5. Let a, b e C. Show that: (a) 2|a||b| < lal2 + |b|2 (b) la...

 

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5. Let a, b e C. Show that: (a) 2|a||b| < lal2 + |b|2 (b) la + b|2 < 2(la|? + |6|2). 6. If (V, <, >) is an F inner product space and Y CV is a subspace. Show that (Y, <, >lyxr) is an F inner product space. 7. If (V, <, >) is a Hilbert space and Y CV is a subspace. Show that Y is a Hilbert space nd only if Y is closed in V 5. Let a, b e C. Show that: (a) 2|a||b| < lal2 + |b|2 (b) la + b|2 < 2(la|? + |6|2). 6. If (V, <, >) is an F inner product space and Y CV is a subspace. Show that (Y, <, >lyxr) is an F inner product space. 7. If (V, <, >) is a Hilbert space and Y CV is a subspace. Show that Y is a Hilbert space nd only if Y is closed in V

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