Spectral synthesis in regular Banach algebras |
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Authors: | Aharon Atzmon |
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Institution: | (1) Department of Mathematics, Tel Aviv University, Israel |
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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.
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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Keywords: | |
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