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MSMalekan
MSMalekan
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Let $G$ be a locally compact group and $A$ be a Banach algebra. By $L^1(G,A)$ and $M(G,A)$ we denote the $A$-valued group, and measure algebra.

  1. Is $M(G,A)$ a Banach algebra (with convolution as the product)?
  2. Let $B$ be a Banach algebra contains $A$ as an ideal. Is $L^1(G,A)$ an ideal of $M(G,B)$?

Let $G$ be a locally compact group and $A$ be a Banach algebra. By $L^1(G,A)$ and $M(G,A)$ we denote the $A$-valued group, and measure algebra.

  1. Is $M(G,A)$ a Banach algebra?
  2. Let $B$ be a Banach algebra contains $A$ as an ideal. Is $L^1(G,A)$ an ideal of $M(G,B)$?

Let $G$ be a locally compact group and $A$ be a Banach algebra. By $L^1(G,A)$ and $M(G,A)$ we denote the $A$-valued group, and measure algebra.

  1. Is $M(G,A)$ a Banach algebra (with convolution as the product)?
  2. Let $B$ be a Banach algebra contains $A$ as an ideal. Is $L^1(G,A)$ an ideal of $M(G,B)$?
Source Link
MSMalekan
MSMalekan
  • 2.1k
  • 1
  • 10
  • 19

About vector valued measure algebras

Let $G$ be a locally compact group and $A$ be a Banach algebra. By $L^1(G,A)$ and $M(G,A)$ we denote the $A$-valued group, and measure algebra.

  1. Is $M(G,A)$ a Banach algebra?
  2. Let $B$ be a Banach algebra contains $A$ as an ideal. Is $L^1(G,A)$ an ideal of $M(G,B)$?