In functional analysis, the adjoint of an operator is a fundamental concept that involves a linear mapping related to the inner product structure of a space. Specifically, if you have a linear operator between two Hilbert spaces, the adjoint operator captures how the original operator interacts with the inner products in these spaces, effectively reversing its action in a specific sense. Understanding adjoints is essential when discussing properties of self-adjoint, unitary, and normal operators, as they provide insights into the spectral theory and stability of these operators.
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