Multipliers and local spectral theory
For a multiplier on a semisimple commutative Banach algebra, the decomposability in the sense of Foiaş will be related to certain continuity properties and growth conditions of its Gelfand transform on the spectrum of the multiplier algebra. If the multiplier algebra is regular, then all multipliers will be seen to be decomposable. In general, an important tool will be the hull-kernel topology on the spectrum of the typically nonregular multiplier algebra. Our investigation involves various closed...
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