Discussion :: GATE Mathematics
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Let c00 be the vector space of all complex sequences having finitely many non-zero terms. Equip c00 the inner product 〈x, y〉 =
for all x=(xn) and y=(yn) in c00. Define f: c00 → ℂ by f(x)= 
. Let N be the kernel of f.Which of the following is FALSE?
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A.
f is a continuous linear functional
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B.
"–f"– ≤ Ï€/√6
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C.
There does not exist any y ∈ c00 such that f(x) = 〈x, y〉 for all x ∈ c00
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D.
N⊥ ≠{0}
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Answer : Option D
Explanation :
-NA-
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