Spectral mapping theorem for representations of measure algebras
1997 ◽
Vol 40
(2)
◽
pp. 261-266
◽
Keyword(s):
Let G be a locally compact abelian group, M0(G) be a closed regular subalgebra of the convolution measure algebra M(G) which contains the group algebra L1(G) and ω: M0(G) → B be a continuous homomorphism of M0(G) into the unital Banach algebra B (possibly noncommutative) such that ω(L1(G)) is without order with respect to B in the sense that if for all b ∈ B, b.ω(L1(G)) = {0} implies b = 0. We prove that if sp(ω) is a synthesis set for L1(G) then the equality holds for each μ ∈ M0(G), where sp(ω) denotes the Arveson spectrum of ω, σB(.) the usual spectrum in B, the Fourier-Stieltjes transform of μ.
Keyword(s):
1968 ◽
Vol 64
(4)
◽
pp. 1015-1022
◽
1963 ◽
Vol 106
(3)
◽
pp. 534-534
Keyword(s):
1960 ◽
Vol 4
(4)
◽
pp. 553-574
◽
Keyword(s):
1982 ◽
Vol 5
(3)
◽
pp. 503-512
1994 ◽
Vol 14
(2)
◽
pp. 130-138
◽
Keyword(s):
2007 ◽
Vol 75
(2)
◽
pp. 369-390
◽
Keyword(s):