I would like to describe Gelfand transofrmation of commutative Banach algebra $l^p(\mathbb{N}),p \in [1,\infty)$ with multiplication define by $(a_n)_n(b_n)_n=(a_n b_n)_n$, but I have no idea, how to do it. Any hints ? Thanks
2026-02-22 23:10:54.1771801854
Gelfand transformation of $l^p$
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The Gelfand transform in this case is nothing but the inclusion map $\ell_p\to c_0$ because the point-evaluations are the only non-zero characters on $\ell_p$.