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Adjoint, Symmetric, and Self-adjoint Linear Operators
2019Here we first recall the definition of the adjoint of a linear operator and discuss some related results. Then we shall address the case of compact operators A : H → H, where H is a Hilbert space, and present the Fredholm theorem as an application. The last section is devoted to symmetric operators and self-adjoint operators.
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The Adjoint Representation and the Adjoint Action
2002The purpose of this article is to study in detail the actions of a semisimple Lie or algebraic group on its Lie algebra by the adjoint representation and on itself by the adjoint action. We will focus primarily on orbits through nilpotent elements in the Lie algebra; these are called nilpotent orbits for short.
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