A Hilbert C*-module admitting no frames

Abstract

We show that every infinite-dimensional commutative unital C*-algebra has a Hilbert C*-module admitting no frames. In particular, this shows that Kasparov's stabilization theorem for countably generated Hilbert C*-modules can not be extended to arbitrary Hilbert C*-modules.

Minor change. To appear in Bull. Lond. Math. Soc

References in corpus (1)

• Frames in Hilbert C*-modules and C*-algebras

Cited by in corpus (7)

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• A Hilbert C*-module with extremal properties
• Topological and frame properties of certain pathological $C^{\ast }$-algebras
• Regularity results for classes of Hilbert C*-modules with respect to special bounded modular functionals
• Orthogonality preserving property for pairs of operators on Hilbert $C^{\ast }$-modules
• Frames and operators in Hilbert C*-modules
• Holomorphic Hilbert Bundles and the Frame Existence Problem