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FRAME-LESS HILBERT C*-MODULES
Published online by Cambridge University Press: 07 February 2018
Abstract
We show that if A is a compact C*-algebra without identity that has a faithful *-representation in the C*-algebra of all compact operators on a separable Hilbert space and its multiplier algebra admits a minimal central projection p such that pA is infinite-dimensional, then there exists a Hilbert A1-module admitting no frames, where A1 is the unitization of A. In particular, there exists a frame-less Hilbert C*-module over the C*-algebra $K(\ell^2) \dotplus \mathbb{C}I_{\ell^2}$.
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- Research Article
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- Copyright © Glasgow Mathematical Journal Trust 2018
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