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Let 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 . Then for every , has a vanishing interior Lebesgue measure. If the statement is not generally true. The result is applied to prove a theorem of Rosenthal.
Let be a bounded representation of a commutative Banach algebra . The following spectral sets are studied. : the Gelfand space of the quotient algebra . : the Gelfand space of the operator algebra . : those characters of for which the inequalities , , have a common solution , for any and any finite subset of . A theorem of Beurling on the spectrum of -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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