Spectrum, homomorphisms and multipliers of Lau product of Banach algebras

Abstract

Given Banach algebras $A$, $B$ and a continuous homomorphism $\theta:B\longrightarrow A$ with $\Vert\theta\Vert \leq1$, we obtain characterization of spectrum, homomorphisms and multipliers of $A\times_{\theta}B$, which is a strongly splitting Banach algebra extension of $B$ by $A$. Also we characterize the semisimplicity of these algebras.

Keywords

• spectrum
• homomorphisms
• multipliers
• Lau product
• faithful
• semisimple

References

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