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Weak spectral synthesis in commutative Banach algebras. III

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Kaniuth, Eberhard

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Let A be a regular and semisimple commutative Banach algebra with structure space Delta(A). Continuing the investigations of [7] and [9], we establish various results on weak spectral sets in Delta(A). To each closed subset of Delta(A) we associate a descending sequence of subsets of Delta(A) which proves to be a powerful tool in the study of weak spectral synthesis. Applications concern injection type properties, unions of weak spectral sets and projective tensor products. A number of interesting examples is discussed: algebras of m-times continuously differentiable functions and of Lipschitz functions, and L-1(R-N).

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Elsevier

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Mathematics

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Journal of Functional Analysis

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10.1016/j.jfa.2015.01.004

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