Q6/ Let I₁, I₂ be two bounded operators on H with T²=T₁=T₁ T2 = I₁=I₂₁. Can we say that if (T₁₂-II₂+1₂)² = (₁-T₂ +T₂) and ker(T₁ – T₂T₂ +T₂₁) = R(T₁ −₂+₂), then ₁₂ = LI? (Proof or counter-example with details).

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