CDAM Research Report, LSE-CDAM-2009-06
Contractability of the maximal ideal space of algebras of measures in a half-space
Amol SasaneLet H be the canonical half space in Rn, and let M(H) denote the Banach algebra of all complex Borel measures with support contained in M(H), with the usual addition and scalar multiplication, and with convolution *, and the norm being the total variation. It is shown that the maximal ideal space of M(H), equipped with the Gelfand topology, is contractible as a topological space. In particular, it follows that M(H) is a projective free ring. In fact, for all subalgebras R of M(H) that satisfy a certain mild condition, it is shown that the maximal ideal space of R is contractible. Several examples of such subalgebras are also given.
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