On the spectral theorem for normal operators
1970 ◽
Vol 68
(2)
◽
pp. 393-400
◽
Keyword(s):
It has been known for some time that one can construct a proof of the spectral theorem for a normal operator on a Hilbert space by applying the Gelfand representation theorem to the Abelian von Neumann algebra generated by the normal operator, and using the fact that the maximal ideal space of an Abelian von Neumann algebra is extremely disconnected. This, in fact, is the spirit of the monograph (8). On the other hand, it is difficult to find in print accounts of the spectral theorem from this viewpoint and, in particular, the treatment in (8) uses a considerable amount of measure theory and does not have the proof of the spectral theorem as its main objective.
1988 ◽
Vol 45
(3)
◽
pp. 287-295
Keyword(s):
1963 ◽
Vol 59
(4)
◽
pp. 727-729
◽
1965 ◽
Vol 17
◽
pp. 1030-1040
◽
Keyword(s):
1971 ◽
Vol 23
(5)
◽
pp. 849-856
◽
1979 ◽
Vol 31
(5)
◽
pp. 1012-1016
◽
Keyword(s):
1982 ◽
Vol 34
(6)
◽
pp. 1245-1250
◽
Keyword(s):
1966 ◽
Vol 18
◽
pp. 897-900
◽
1969 ◽
Vol 21
◽
pp. 1421-1426
◽