Doubly stochastic right multipliers
1984 ◽
Vol 7
(3)
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pp. 477-489
Keyword(s):
LetP(G)be the set of normalized regular Borel measures on a compact groupG. LetDrbe the set of doubly stochastic (d.s.) measuresλonG×Gsuch thatλ(As×Bs)=λ(A×B), wheres∈G, andAandBare Borel subsets ofG. We show that there exists a bijectionμ↔λbetweenP(G)andDrsuch thatϕ−1=m⊗μ, wheremis normalized Haar measure onG, andϕ(x,y)=(x,xy−1)forx,y∈G. Further, we show that there exists a bijection betweenDrandMr, the set of d.s. right multipliers ofL1(G). It follows from these results that the mappingμ→Tμdefined byTμf=μ∗fis a topological isomorphism of the compact convex semigroupsP(G)andMr. It is shown thatMris the closed convex hull of left translation operators in the strong operator topology ofB[L2(G)].
1976 ◽
Vol 80
(2)
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pp. 269-276
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Keyword(s):
1977 ◽
Vol 29
(3)
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pp. 626-630
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Keyword(s):
Keyword(s):
2013 ◽
Vol 94
(2)
◽
pp. 202-221
Keyword(s):
1964 ◽
Vol 15
(2)
◽
pp. 256-256
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2011 ◽
Vol 381
(2)
◽
pp. 678-688
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