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A property of Fourier Stieltjes transforms on the discrete group of real numbers

Yngve Domar — 1970

Annales de l'institut Fourier

Let μ be a Fourier-Stieltjes transform, defined on the discrete real line and such that the corresponding measure on the dual group vanishes on the set of characters, continuous on R . Then for every ϵ > 0 , { x R | Re ( μ ( x ) ) > ϵ } has a vanishing interior Lebesgue measure. If ϵ = 0 the statement is not generally true. The result is applied to prove a theorem of Rosenthal.

Three spectral notions for representations of commutative Banach algebras

Yngve DomarLars-Ake Lindahl — 1975

Annales de l'institut Fourier

Let T be a bounded representation of a commutative Banach algebra B . The following spectral sets are studied. Λ 1 ( T ) : the Gelfand space of the quotient algebra B / Ker T . Λ 2 ( T ) : the Gelfand space of the operator algebra Im T . Λ 3 ( T ) : those characters φ of B for which the inequalities T b x - b ^ ( φ ) x < ϵ x , b F , have a common solution x 0 , for any ϵ > 0 and any finite subset F of B . A theorem of Beurling on the spectrum of L -functions and results of Slodkowski and Zelazko on joint topological divisors of zero appear as special cases of our theory by...

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