In this paper, we determine the character space of vector-valued Lipschitz algebra Lipd(X, E), where (X, d) is any metric and E a certain unital semisimple commutative *-Banach algebra.

let $t$ be a bounded operator on the banach space $x$ and $ph$ be an analytic self-map of the unit disk $bbb{d}$‎. ‎we investigate some operator theoretic properties of‎ ‎bilateral composition operator $c_{ph‎, ‎t}‎: ‎f ri t circ f circ ph$ on the vector-valued hardy space $h^p(x)$ for $1 leq p leq‎ ‎+infty$.‎ ‎compactness and weak compactness of $c_{ph‎, ‎t}$ on $h^p(x)$‎ ‎are characterized an...

This paper contains the equivalence between tvs-G cone metric and G-metric using a scalarization function $\zeta_p$, defined over locally convex Hausdorff topological vector space. ensures that most studies on existence uniqueness of fixed-point theorems space spaces are equivalent. We prove vector-valued version scalar-valued those spaces. Moreover, we present if real Banach is considered inst...