Hilbert algebras
1950; Tohoku University; Volume: 2; Issue: 1 Linguagem: Inglês
10.2748/tmj/1178245666
ISSN2186-585X
Autores Tópico(s)Polynomial and algebraic computation
Resumoa proper 1A*'algebra ξ> * £> is a Hubert space and a τing subject to the conditions: 1) if aχ=^0 for all x ε φ, then a = 0, and 2) for any a e § there is a?' e © such that for all x, j ε ξ>, and proved that if ξ> satisfies the condition (B) sup || xy || < + oo, lί*ll-l|yJ=»i then § is a direct sum of simple 2'Sided ideals Σ *Q\ such that «ξ> P JL ©λ for λεΛ />4=λ and ξ)λ is isometric to a full-matrix algetra : for some set Λ all complex valued functions a (λ, p) (λ, p e A) with Σ \a (λ, i o) λ p constitute a proper H*-algebra, being called a full-matrix algebra, if we put Λ£ (λ, p) = Έι a (λ, T) 6 (T, I??), Λ* (λ, p) = a (p, λ), λ pfor some positive number a, wich we shall call the order of a full-matrix algebra.He used the condition (B) essentially in his proof, while it will be proved that any H* -algebra satisfies the condition (B) (cf.§2).He remarked further that a group ring on a compact group is a proper H '-algebra: let © be a compact group.All complex valued measurable functions a (σ) (σ ε ©) with j| a (σ) ! 2 dσ < + oofor Haar measure constitute a proper H*-algebra if we put *)
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