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Spectral synthesis in regular Banach algebras

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Abstract

We prove that every locally compact non-discrete abelian groupG contains a compact subsetE such thatA(E) — the restriction algebra ofA(G) toE — admits spectral synthesis, although it contains a closed, regular, self-adjoint subalgebra which is isomorphic to an algebra of infinitely differentiable functions on [−1, 1]. We also give some general results concerning the failure of spectral synthesis in regular Banach algebras.

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Authors and Affiliations

  1. Department of Mathematics, Tel Aviv University, Israel

    Aharon Atzmon

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  1. Aharon Atzmon
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Additional information

This paper is a part of the author’s Ph.D. thesis prepared at the Hebrew University of Jerusalem, under the supervision of Professor Y. Katznelson, to whom the author wishes to express his gratitude for his valuable remarks, and the interest he showed in the preparation of this paper.

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Atzmon, A. Spectral synthesis in regular Banach algebras. Israel J. Math. 8, 197–212 (1970). https://doi.org/10.1007/BF02771558

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  • DOI: https://doi.org/10.1007/BF02771558

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