Want to take part in these discussions? Sign in if you have an account, or apply for one below
Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.
adjoint operator was in a very poor state, so I copied in at least the start of self-adjoint operator.
added (here) a quote by MacLane on the history of the notion:
Two of von Neummann’s papers on this topic [Hilbert spaces] had been accepted in the Mathematische Annalen, a journal of Springer Verlag. Marshall Stone had seen the manuscripts, and urged von Neumann to observe that his treatment of linear operators $T$ on a Hilbert space could be much more effective if he were to use the notion of an adjoing $T^ast$ to the linear transformation $T$ — one for which the now familiar equation
$\;\;\;\;\; \langle T a, b \rangle \;=\; \langle a, T^\ast b \rangle$
would hold for all suitable $a$ and $b$. Von Neumann saw the point immediately, as was his wont, and wishes to withdraw the papers before publication. They were already set up in type; Springer finally agreed to cancel them on the condition that von Neumann write for them a book on the subject — which he soon did [1932].
This story (told to me by Marshall Stone) illustrates the important conceptual advance represented by the definition of adjoint operators. &lbrack…] I have written elsewhere [1970] that it is a step toward the subsequent description of a functor $G$ right adjoint to a functor $F$, in terms of a natural isomorphism
$\;\;\;\;\; hom(F a, b) \;\simeq\; hom(a, G b)$
between hom-sets in suitable categories.
1 to 3 of 3