Multipliers of Commutative $$\varvec{F}$$ F -Algebras of Continuous Vector-Valued Functions

Multipliers of Modules of Continuous Vector-Valued Functions

“…For its justification, we mention that as a consequence of the vector-valued versions of Stone-Weierstrass theorem [8,12,15], 0 ( ) ⊗ is -dense in 0 ( , ) in each of the following cases. Recall that if ∈ ( 0 ( , )), then ( ⋅ ) = ⋅ ( ) for ∈ 0 ( , ) and ∈ ( [16,Lemma 4.5]). We also mention that if ( , ) is an -normed algebra having a minimal approximate identity, then, by ([16,Lemma 4.4]), 0 ( , ) has an approximate identity and hence it is a faithful topological -module.…”

“…Recall that if ∈ ( 0 ( , )), then ( ⋅ ) = ⋅ ( ) for ∈ 0 ( , ) and ∈ ( [16,Lemma 4.5]). We also mention that if ( , ) is an -normed algebra having a minimal approximate identity, then, by ([16,Lemma 4.4]), 0 ( , ) has an approximate identity and hence it is a faithful topological -module. Consequently, for any ∈ ( 0 ( , )), ( ) = ( ) = ( ) for all , ∈ 0 ( , ); we will write…”

“…Corollary 19 (see [16]). Let be a locally compact Hausdorff space and = ( , ) a commutative complete -normed algebra with a minimal approximate identity.…”