Order convolution and vector-valued multipliers

• Autorzy: U. B. Tewari
• Języki publikacji: EN

Abstrakty

EN

Let I = (0,∞) with the usual topology. For x,y ∈ I, we define xy = max(x,y). Then I becomes a locally compact commutative topological semigroup. The Banach space L¹(I) of all Lebesgue integrable functions on I becomes a commutative semisimple Banach algebra with order convolution as multiplication. A bounded linear operator T on L¹(I) is called a multiplier of L¹(I) if T(f*g) = f*Tg for all f,g ∈ L¹(I). The space of multipliers of L¹(I) was determined by Johnson and Lahr. Let X be a Banach space and L¹(I,X) be the Banach space of all X-valued Bochner integrable functions on I. We show that L¹(I,X) becomes an L¹(I)-Banach module. Suppose X and Y are Banach spaces. A bounded linear operator T from L¹(I,X) to L¹(I,Y) is called a multiplier if T(f*g) = f*Tg for all f ∈ L¹(I) and g ∈ L¹(I,X). In this paper, we characterize the multipliers from L¹(I,X) to L¹(I,Y).

Kategorie tematyczne

• 46E40: Spaces of vector- and operator-valued functions
• 43A22: Homomorphisms and multipliers of function spaces on groups, semigroups, etc.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2007
• Tom: 108
• Numer: 1
• Strony: 53-61

Daty

wydano

2007

Twórcy

autor

U. B. Tewari

• Department of Mathematics and Statistics, Indian Institute of Technology Kanpur, Kanpur 208 016, India

Identyfikatory

DOI

10.4064/cm108-1-5