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We present conditions under which the Gel’fand transform E ∧ , of locally m-convex algebra E, is a dense subalgebra of C c (M (E)) . The partition of unity and the local theorem are given for a commutative unital locally m-convex algebra. [ABSTRACT FROM AUTHOR]

This paper deals with the automatic continuity of multiplicative polynomial operators on a class of topological algebras. Several results are derived in this direction. We also support our results by some examples.

In this paper, we characterize the weighted generalization of the space of continuous functions vanishing at infinity and correct some wrong results in the paper. Let X be a locally compact space and ν is an arbitrary weight (non‐negative function) on X. We give a correct and comprehensive definition of the weighted generalization C0ν(X)$C_0^\nu (X)$ of C0(X)$C_0(X)$, and show that it is a seminormed space with respect to the canonical seminorm ∥f∥ν=supx∈X|f(x)|$\Vert f\Vert _\nu =\sup _{x\in X}|f(x)|$, where f∈C0ν(X)$f\in C_0^\nu (X)$. We find conditions on ν under which C0ν(X)$C_0^\nu (X)$, with respect to ∥.∥ν$\Vert.\Vert _\nu$, becomes a normed space or a Banach space or an algebra, or a topological algebra, respectively. [ABSTRACT FROM AUTHOR]

This paper deals with the automatic continuity of multiplicative polynomial operators on a class of topological algebras. Several results are derived in this direction. We also support our results by some examples. [ABSTRACT FROM AUTHOR]

This paper presents dual B-topologies that are determined by filterbase and some sets in a dual B-algebra. Also, some properties of a filterbase in a dual B-topological space are provided. In particular, a commutative dual B-topological space and a symmetric B-topological space are topological dual B-algebras. [ABSTRACT FROM AUTHOR]

In this paper, we consider the notion of quasi-multipliers to the general topological algebra setting, not necessarily normed or locally convex. We discuss the quasi-uniform and quasi-strong operator topologies on the algebra QM(A) of all bilinear and jointly continuous quasi-multipliers on A and study their various properties. [ABSTRACT FROM AUTHOR]

We present a general survey on formal power series over topological algebras, along with some perspectives which are not easily found in the literature. [ABSTRACT FROM AUTHOR]

We present a general survey on formal power series over topological algebras, along with some perspectives which are not easily found in the literature.