Operator Valued Measures as Multipliers of L1(I,X) with order Convolution
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Abstract Let I = (0;∞) with the usual topology and product as max multiplication. Then I becomes a locally compact topo- logical semigroup. Let X be a Banach Space. Let L1(I;X) be the Banach space of X-valued measurable functions f such that ,we define It turns out that ƒ ∗ g ∈ L1(I;X) and L1(I;X) becomes an L1(I)-Banach module. A bounded linear operator T on L1(I;X) is called a multiplier of L1(I;X) if T(f ∗ g) = f ∗ Tg for all f ∈ L1(I) and g ∈ L1(I;X). We characterize the multipliers of L1(I;X) in terms of operator valued measures with point-wise finite variation and give an easy proof of some results of Tewari[12].
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1967 ◽
Vol 7
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pp. 1-6
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1991 ◽
Vol 14
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pp. 611-614
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1969 ◽
Vol 21
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pp. 592-594
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1992 ◽
Vol 46
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pp. 179-186
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1997 ◽
Vol 56
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pp. 303-318
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