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Let A be a C*-algebra and let X be a full (right) Hilbert A-module. It is shown that if the spectrum A of A is discrete, then every closed κ(X)-A-submodule of X is complemented in X, and conversely that if Â is a T 1 -space and if every closed κ(X)-A-submodule of X is complemented in X, then A is discrete.

Discrete spectra of $C^{*}$-algebras and complemented submodules in Hilbert $C^{*}$-modules

Discrete spectra of $C^{}$-algebras and complemented submodules in Hilbert $C^{}$-modules