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Derivations and automorphisms of $L\sp{1}\,(0,\,1)$

1969
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Transactions of the American Mathematical Society
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In this paper we investigate the derivations and automorphisms of the radical algebra L\0, 1), in which the product off and g is given by Recall that if X is an algebra, a linear map D is a derivation provided D(xy) =xD(y) + D(x)y for all x, ye X. All automorphisms and derivations in this paper are assumed to be bounded. In §1 we show that every derivation has the form Df=xf* p, where \p\[0, t] = 0(1/(1 -t)) as t -*■ 1 ~ ; D is quasinilpotent if and only if p has no mass at 0. We also determine

doi:10.1090/s0002-9947-1969-0233210-4
fatcat:zidsif25bfhf3mj5c3wjtlsr6e