Multipliers for Certain Convolution Measure Algebras

Lahr, Charles D.

doi:10.2307/1996432

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Isometric Multipliers Of Lx(s)1

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1976

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“…Let S2 = Sx U (e); clearly, fi(S2) = S2. <D1L(/,(5'1)) = /1(S2(5'1)) since lx(Sx) has a bounded approximate identity [4], and y\L(lx(S2)) = lx(S2). Certainly, 91t(/,(Sx)) is isomorphic (isometrically) to 'DUi/,^)), but lx(Sx) is not isomorphic to lx(S2).…”

Section: Isometric Multipliers Of Lx(s)mentioning

confidence: 99%

Isometric multipliers and isometric isomorphisms of $l\sb{1}(S)$

Lahr¹

1976

Proc. Amer. Math. Soc.

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Let S be a commutative semigroup and 0(S) the multiplier semigroup of 5. It is shown that T is an isometric multiplier of lx(S) if and only if there exists an invertible element o S Í2(S) and a complex number X of unit modulus such that T(a) = \^,xes a(x)Sa,x, for each a-2,es «M*x e'l(S)-Also, if 5, and S2 are commutative semigroups, and L is an isometric isomorphism of /|(5,) into/,(S2), then it is proved that there exist a semicharacter x, IxMI = 1 Ior all x £ Sx, and an isomorphism /' of S, onto S2 such that L(a) = 2 x(*)«(*)*f(x) for each a = 2xes, a(x)sx e 'i(^i)

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Section: Isometric Multipliers Of Lx(s)mentioning

confidence: 99%

Isometric multipliers and isometric isomorphisms of $l\sb{1}(S)$

Lahr¹

1976

Proc. Amer. Math. Soc.

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show abstract

Multipliers for Certain Convolution Measure Algebras

Cited by 1 publication

References 10 publications

Isometric multipliers and isometric isomorphisms of $l\sb{1}(S)$

Isometric multipliers and isometric isomorphisms of $l\sb{1}(S)$

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