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FRAME-LESS HILBERT C*-MODULES

Part of: Nontrigonometric harmonic analysis Selfadjoint operator algebras

Published online by Cambridge University Press:  07 February 2018

M. B. ASADI ,
M. FRANK Open the ORCID record for M. FRANK [Opens in a new window]  and
Z. HASSANPOUR-YAKHDANI
M. B. ASADI
Affiliation:
School of Mathematics, Statistics and Computer Science, College of Science, University of Tehran, Tehran, Iran School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O. Box: 19395-5746, Tehran, Iran e-mail: mb.asadi@khayam.ut.ac.ir
M. FRANK
Affiliation:
Hochschule für Technik Wirtschaft und Kultur (HTWK) Leipzig, Fakultät IMN PF 301166, 04251 Leipzig, Germany e-mail: michael.frank@htwk-leipzig.de
Z. HASSANPOUR-YAKHDANI
Affiliation:
School of Mathematics Statistics and Computer Science, College of Science, University of Tehran, Tehran, Iran e-mail: z.hasanpour@ut.ac.ir
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Abstract

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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 $K(\ell^2) \dotplus \mathbb{C}I_{\ell^2}$.

MSC classification

Primary: 46L08: $C^*$-modules
Secondary: 42C15: General harmonic expansions, frames 46L05: General theory of $C^*$-algebras
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 61 , Issue 1 , January 2019 , pp. 25 - 31
Copyright
Copyright © Glasgow Mathematical Journal Trust 2018 

References

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