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2. Hermitian adjoint - Wikipedia

   en.wikipedia.org/wiki/Hermitian_adjoint

   In mathematics, specifically in operator theory, each linear operator on an inner product space defines a Hermitian adjoint (or adjoint) operator on that space according to the rule A x , y = x , A ∗ y , {\displaystyle \langle Ax,y\rangle =\langle x,A^{*}y\rangle ,}

3. Linear Operators (book) - Wikipedia

   en.wikipedia.org/wiki/Linear_Operators_(book)

   Linear Operators is a three-volume textbook on the theory of linear operators, written by Nelson Dunford and Jacob T. Schwartz. The three volumes are (I) General Theory; (II) Spectral Theory, Self Adjoint Operators in Hilbert Space; and (III) Spectral Operators. The first volume was published in 1958, the second in 1963, and the third in 1971.

4. Self-adjoint operator - Wikipedia

   en.wikipedia.org/wiki/Self-adjoint_operator

   In practical terms, having an essentially self-adjoint operator is almost as good as having a self-adjoint operator, since we merely need to take the closure to obtain a self-adjoint operator. In physics, the term Hermitian refers to symmetric as well as self-adjoint operators alike. The subtle difference between the two is generally overlooked.

5. Adjoint - Wikipedia

   en.wikipedia.org/wiki/Adjoint

   In mathematics, the term adjoint applies in several situations. Several of these share a similar formalism: if A is adjoint to B, then there is typically some formula of the type (Ax, y) = (x, By). Specifically, adjoint or adjunction may mean: Adjoint of a linear map, also called its transpose in case of matrices

6. Von Neumann's theorem - Wikipedia

   en.wikipedia.org/wiki/Von_Neumann's_theorem

   Let and be Hilbert spaces, and let : ⁡ be an unbounded operator from into . Suppose that is a closed operator and that is densely defined, that is, ⁡ is dense in . Let : ⁡ denote the adjoint of .

7. Trace inequality - Wikipedia

   en.wikipedia.org/wiki/Trace_inequality

   For operators on an infinite dimensional Hilbert space we require that they be trace class and self-adjoint, in which case similar definitions apply, but we discuss only matrices, for simplicity.