The linear functionals on fundamental locally multiplicative topological algebras

In this paper we study the dual space of fundamental locally multiplicative topological algebras and prove some results for linear and multiplicative linear functionals on these algebras. An investigation on locally compactness of the carrier space of these algebras is the last part of this note.

The linear functionals on fundamental locally multiplicative topological algebras

In this paper we study the dual space of fundamental locally multiplicative topological algebras and prove some results for linear and multiplicative linear functionals on these algebras. An investigation on locally compactness of the carrier space of these algebras is the last part of this note.

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  • Suppose f is a linear functional on complex Banach algebra A, and let x∈ A with x ≤ 1. Choose xk∈ A with xk < 1 such that xk→ x, Then ∃b > 1 such that bnxkn→ 0 and therefore |f(xk)| ≤ v(f) and so|f(x)| ≤ v(f), i.e f ≤ v(f). 2