Teaching JKPSC Lecturership Mock Test Series 2024-25 Mathematical Science Analysis Normed Linear Spaces
Let {ek : k ∈ ℕ} be an orthonormal basis for a Hilbert space H.
Define fk = ek + ek+1, k ∈ ℕ and gj = \(\Sigma_{n=1}^j(-1)^{n+1}e_n, \) j ∈ ℕ.
Then \(\rm \Sigma_{k=1}^\infty|⟨g_j , f_k⟩|^2\) =
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