Multipliers of modules of continuous vector-valued functions. (English) Zbl 1472.46048

Summary: In [Pac. J. Math. 11, 1131–1149 (1961; Zbl 0127.33302)], J.-K. Wang showed that if \(A\) is the commutative \(C^*\)-algebra \(C_0(X)\) with \(X\) a locally compact Hausdorff space, then \(M(C_0(X)) \cong C_b(X)\). Later, this type of characterization of multipliers of spaces of continuous scalar-valued functions has also been generalized to algebras and modules of continuous vector-valued functions by several authors. In this paper, we obtain further extension of these results by showing that \[\text{H} \text{o} \text{m}_{C_0(X, A)}(C_0(X, E), C_0(X, F)) \simeq C_{s, b}(X, \text{H} \text{o} \text{m}_A(E, F)),\] where \(E\) and \(F\) are \(p\)-normed spaces which are also essential isometric left \(A\)-modules with \(A\) being a certain commutative \(F\)-algebra, not necessarily locally convex. Our results unify and extend several known results in the literature.


46H25 Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX)
46E40 Spaces of vector- and operator-valued functions


Zbl 0127.33302
Full Text: DOI


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