On Strong Spectrally Bounded LMC*‐Algebras

A locally m ‐convex algebra E ≡ ( E , ( p α ); α ∈ A ) is called “strong spectrally bounded” if supp α ( x ) < ∞, for every x ∈ E. A locally m ‐convex C *‐algebra of the last kind always accepts a faithful representation, say φ, with a continuous inverse, such that ‖‖φ( x )‖‖ = supp α , for al x ∈ E . Particularly, in case E is moreover barrelled, φ is also continuous, E becoming thus a *‐subalgebra of a concrete C *‐algebra ℒ( H ), H a Hilbert space.