A Note on a Theorem of K. G. Wolfson
نویسنده
چکیده
Theorem. A commutative B*-algebra K containing an identity e (with \\k*-k\\ =\\k\\2for all &GP and ||e|| =1) is isomorphic (in a norm and * preserving manner) to an algebra B(X) of all bounded complexvalued functions on an essentially unique set X if and only if: (1) Every nonzero closed ideal of K contains a minimal ideal; (2) The sum of two annulets is an annulet. An annulet is here understood to be an ideal I of K with which is associated a subset GCP such that
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References 1. I. Gelfand, Normierte Ringe, Rec. Math. (Mat. Sbornik) N.S. vol. 9 (1941) pp. 3-24. 2. I. Gelfand and M. Neumark, On the embedding of normed rings into the ring of operators in Hubert Space, Rec. Math. (Mat. Sbornik) N.S. vol. 12 (1943) pp. 197213. 3. L. J. Heider, A note on a theorem of K. G. Wolf son, Proc. Amer. Math. Soc. vol. 6 (1955) pp. 305-308. 4. N. Jacobson, The theory o...
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