Adjoints, Symmetric Operators

Mohammed Hichem Mortad
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Mohammed Hichem Mortad: University of Oran 1

Chapter Chapter 20 in Counterexamples in Operator Theory, 2022, pp 345-374 from Springer

Abstract: Abstract Let A : D(A) ⊂ H → K be a densely defined linear operator, where H and K are two Hilbert spaces. Then D(A ∗) is the set constituted of all y ∈ K for which there exists a z ∈ H such that 〈 A x , y 〉 = 〈 x , z 〉 , ∀ x ∈ D ( A ) . $$\displaystyle \langle Ax,y\rangle =\langle x,z\rangle ,\forall x\in D(A). $$ We set for each y ∈ D(A ∗), A ∗ y = z. The (linear) operator A ∗ then obtained is called the adjoint of A.

Date: 2022
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DOI: 10.1007/978-3-030-97814-3_20

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