Theoretical analysis establishes characterizations and a structure theorem for unbounded antilinear normal operators in complex Hilbert spaces, highlighting new foundations for operator theory.
An operator A on a complex Hilbert space H H is called antilinear if $$A(x+y)=Ax+Ay$$ A ( x + y ) = A x + A y and A(λ x)=λ ̄ Ax A ( λ x ) = λ ¯ A x for x,y∈ D(A) x , y ∈ D ( A ) and λ ∈ C λ ∈ C . We investigate some classes of densely defined antilinear unbounded operators, especially antilinear normal operators. We give various characterizations of antilinear normal operators and study a class of such operators in detail. Our main result is a structure theorem for unbounded antilinear normal operators.
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Konrad Schmüdgen (2026) studied this question.
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