Operator valued measures as multipliers of L₁ (I, X) with order convolution

• Autorzy: Chaurasia P. K.

Identyfikatory

DOI

10.1515/fascmath-2015-0003

• Języki publikacji: EN

Abstrakty

EN

Let I = (0, ∞) with the usual topology and product as max multiplication. Then I becomes a locally compact topological semigroup. Let X be a Banach Space. Let L₁(I,X) be the Banach space of X-valued measurable functions ƒ such that ʃ₀^∞ǁƒ (t)ǁdt < ∞. If ƒ ϵ L₁(I) and g ϵ L₁(I, X), we define f * g(s) = ƒ (s) ʃ g(t)dt + g(s) ʃ_0s ƒ (t)dt. It turns out that f * g ϵ 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 ƒ ϵ L₁ (I) and g ϵ 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].

Słowa kluczowe

EN

vector valued multiplier; operator valued Measure; order convolution

• Wydawca: Wydawnictwo Politechniki Poznańskiej
• Czasopismo: Fasciculi Mathematici
• Rocznik: 2015
• Tom: Nr 54
• Strony: 41--58
• Opis fizyczny: Bibliogr. 13 poz.

Twórcy

autor

Chaurasia P. K.

• Department of Education in Science and Mathematics Regional Institute of Education (NCERT) 305004 Ajmer, India

Bibliografia

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