George Mackey, 1916-2006

[F W Lawvere <wlawvere@buffalo.edu>]

Dear friends,

    Together with many others, I am deeply saddened by the death of
George Mackey. For far too long, I had been delaying the trip to see him
and continue our discussions which had started in the "Weyl'sche Kammer"
at the ETH in Zurich and continued in the physics center in Trieste. Long
before I met him, his insights into mathematics and into quantum mechanics
had been informing my own thinking. It was the study of his book on
quantum mechanics in 1967 which led directly to the joint course by
Saunders Mac Lane and me at the University of Chicago. But his relation to
category theory goes back much further than that, as Saunders and Sammy
had explained to me.

    George Mackey's Ph.D. thesis displayed remarkable thinking of a
categorical nature, even before categories had been defined. Specifically,
the fact that the category of Banach spaces and continuous linear maps is
fully embedded into a category of pairings of abstract vector spaces,
together with the definition and use of "Mackey convergence" of a sequence
in a "bornological" vector space were discovered there and have played a
basic role in some form in nearly every book on functional analysis since.
What is perhaps unfortunately not clarified in nearly every book on
functional analysis, is that these concepts are intensely categorical in
character and that further enlightenment would result if they were so
clarified.

   And who, despite initial skepticism, permitted the first paper giving
an exposition of the theory of categories to see the light of day in the
Transactions of the AMS in 1945? None other than the referee, George
Whitelaw Mackey.

   Sincerely,
		F. William Lawvere


************************************************************
F. William Lawvere
Mathematics Department, State University of New York
244 Mathematics Building, Buffalo, N.Y. 14260-2900 USA
Tel. 716-645-6284
HOMEPAGE:  http://www.acsu.buffalo.edu/~wlawvere
************************************************************