Abstract:For a commutative unital ring R, and n P N, let SL n pRq denote the special linear group over R, and E n pRq the subgroup of elementary matrices. Let M `be the Banach algebra of all complex Borel measures on r0, `8q with the norm given by the total variation, the usual operations of addition and scalar multiplication, and with convolution. It is shown that SL n pAq " E n pAq for Banach subalgebras A of M `that are closed under the operation M `Q µ Þ Ñ µ t , t P r0, 1s, where µ t pEq :" ş E p1 ´tq x dµpxq for t… Show more
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