Professor Robert Archbold

MA, MMath (Cantab) PhD (Newcastle)

Emeritus Professor

About

Email Address: r.archbold@abdn.ac.uk
Office Address: Fraser Noble Building: Room 140 in the Institute of Mathematics (first floor).
School/Department: School of Natural and Computing Sciences

External Memberships

Research

Research Overview

I am a mathematical analyst with research interests in functional analysis, operator algebras and topological groups.

Publications

Page 1 of 2 Results 1 to 25 of 38

Local variants of the Dixmier property and weak centrality for C*-algebras
2023 - Published
Archbold, R. J., Gogic, I., Robert, L.
International Mathematics Research Notices, vol. 2023, no. 2, pp. 1483–1513
Contributions to Journals: Articles
- [ONLINE] DOI: https://doi.org/10.1093/imrn/rnab275
- [OPEN ACCESS] http://aura.abdn.ac.uk/bitstream/2164/19411/1/Archbold_etal_IMRN_Local_Variants_Of_AAM.pdf
The centre-quotient property and weak centrality for C^∗-algebras
2022 - Published
Archbold, R. J., Gogic, I.
International Mathematics Research Notices, vol. 2022, no. 2, pp. 1173–1216
Contributions to Journals: Articles
- [ONLINE] DOI: https://doi.org/10.1093/imrn/rnaa133
- [OPEN ACCESS] http://aura.abdn.ac.uk/bitstream/2164/16654/1/Archbold_et_al_IMRN_TheCentreQuotient_AAM.pdf
Minimal primal ideals in the inner corona algebra of a C_{0}(X)-algebra
2020 - Published
Archbold, R. J., Somerset, D. W. B.
Houston Journal of Mathematics, vol. 46, no. 1, pp. 117-150
Contributions to Journals: Articles
- [ONLINE] https://www.math.uh.edu/~hjm/restricted/pdf46(1)/07archbold.pdf
- [OPEN ACCESS] http://aura.abdn.ac.uk/bitstream/2164/13585/1/hjm_archbold_somerset_inner_corona_revised4_.pdf
Maximally unitarily mixed states on a C*-algebra
2018 - Published
Archbold, R. J., Robert, L., Tikuisis, A.
Journal of Operator Theory, vol. 80, no. 1, pp. 187-211
Contributions to Journals: Articles
- [ONLINE] DOI: https://doi.org/10.7900/jot.2017sep24.2168
Topological Frobenius reciprocity for representations of nilpotent groups and motion groups
2017 - Published
Archbold, R. J., Kaniuth, E.
Journal of Lie Theory, vol. 27, no. 3, pp. 745-769
Contributions to Journals: Articles
- [ONLINE] http://www.heldermann.de/JLT/JLT27/JLT273/jlt27038.htm
The Dixmier property and tracial states for C*-algebras
2017 - Published
Archbold, R., Robert, L., Tikuisis, A.
Journal of Functional Analysis, vol. 273, no. 8, pp. 2655-2718
Contributions to Journals: Articles
- [ONLINE] DOI: https://doi.org/10.1016/j.jfa.2017.06.026
- [OPEN ACCESS] http://aura.abdn.ac.uk/bitstream/2164/9199/1/The_Dixmier_property_and_tracial_states_for_C_algebras.pdf
The Inner Corona Algebra of a C0(X)-Algebra
2017 - Published
Archbold, R. J., Somerset, D. W. B.
Proceedings of the Edinburgh Mathematical Society, vol. 60, no. 2, pp. 299-318
Contributions to Journals: Articles
- [ONLINE] DOI: https://doi.org/10.1017/S0013091516000171
- [OPEN ACCESS] http://aura.abdn.ac.uk/bitstream/2164/8353/1/InnerCorona_revised_ArchboldSomerset.pdf
Norms of inner derivations for multiplier algebras of C ∗ -algebras and group C ∗ -algebras, II
2015 - Published
Archbold, R. J., Kaniuth, E., Somerset, D. W. B.
Advances in Mathematics, vol. 280, pp. 225-255
Contributions to Journals: Articles
- [ONLINE] DOI: https://doi.org/10.1016/j.aim.2015.04.019
- [OPEN ACCESS] http://aura.abdn.ac.uk/bitstream/2164/9505/1/Norms_of_inner_dervations_for_multiplier_algebras_of_C_algebras_and_group_C_algebras_II.pdf
The C*-algebras of compact transformation groups
2015 - Published
Archbold, R. J., an Huef, A.
Canadian journal of mathematics. Journal canadien de mathématiques, vol. 67, no. 3, pp. 481-506
Contributions to Journals: Articles
- [ONLINE] DOI: https://doi.org/10.4153/CJM-2014-039-x
Minimal Primal Ideals in the Multiplier Algebra of a C₀(X)-algebra
2015 - Published
Archbold, R. J., Somerset, D. W. B.
Chapters in Books, Reports and Conference Proceedings: Conference Proceedings
- [ONLINE] DOI: https://doi.org/10.1007/978-3-319-18494-4_2
Separation properties in the primitive ideal space of a multiplier algebra
2014 - Published
Archbold, R. J., Somerset, D. W. B.
Israel Journal of Mathematics, vol. 200, no. 1, pp. 389-418
Contributions to Journals: Articles
- [ONLINE] DOI: https://doi.org/10.1007/s11856-014-0022-6
- [OPEN ACCESS] http://aura.abdn.ac.uk/bitstream/2164/4577/1/ArchboldSomerset_SeparationProperties_Revised.pdf
Spectral synthesis in the multiplier algebra of a C_0(X)-algebra
2014 - Published
Archbold, R. J., Somerset, D. W. B.
Quarterly Journal of Mathematics, vol. 65, no. 1, pp. 1-24
Contributions to Journals: Articles
- [ONLINE] DOI: https://doi.org/10.1093/qmath/has048
- [OPEN ACCESS] http://aura.abdn.ac.uk/bitstream/2164/3136/1/ArchSom_QJM5680_accepted.pdf
Strength of convergence in non-free transformation groups
2012 - Published
Archbold, R. J., an Huef, A.
Journal of Functional Analysis, vol. 263, no. 4, pp. 819-845
Contributions to Journals: Articles
- [ONLINE] DOI: https://doi.org/10.1016/j.jfa.2012.05.005
Ideals in the multiplier and corona algebras of a C_o(X)-algebra
2012 - Published
Archbold, R. J., Somerset, D. W. B.
Journal of the London Mathematical Society, vol. 85, no. 2, pp. 365-381
Contributions to Journals: Articles
- [ONLINE] DOI: https://doi.org/10.1112/jlms/jdr053
Norms of inner derivations for multiplier algebras of C*-algebras and group C*-algebras
2012 - Published
Archbold, R. J., Kaniuth, E., Somerset, D. W. B.
Journal of Functional Analysis, vol. 262, no. 5, pp. 2050-2073
Contributions to Journals: Articles
- [ONLINE] DOI: https://doi.org/10.1016/j.jfa.2011.12.015
On the real rank of C*-algebras of nilpotent locally compact groups
2012 - Published
Archbold, R. J., Kaniuth, E.
Mathematica Scandinavica, vol. 110, no. 1, pp. 99-110
Contributions to Journals: Articles
- [ONLINE] http://www.mscand.dk/article/view/15199
- [ONLINE] DOI: https://doi.org/10.7146/math.scand.a-15199
Multiplier algebras of C_0(X)-algebras
2011 - Published
Archbold, R. J., Somerset, D. W. B.
Muenster Journal of Mathematics, vol. 4, pp. 73-100
Contributions to Journals: Articles
- [ONLINE] http://wwwmath.uni-muenster.de/mjm/acc.html
Completely bounded mappings and simplicial complex structure in the primitive ideal space of a C^*-algebra
2009 - Published
Archbold, R. J., Somerset, D. W. B., Timoney, R. M.
Transactions of the American Mathematical Society, vol. 361, no. 3, pp. 1397-1427
Contributions to Journals: Articles
- [ONLINE] DOI: https://doi.org/10.1090/S0002-9947-08-04666-7
Factorial states, upper multiplicity and norms of elementary operators
2008 - Published
Archbold, R. J., Somerset, D. W. B., Timoney, R. M.
Journal of the London Mathematical Society, vol. 78, no. 3, pp. 707-722
Contributions to Journals: Articles
- [ONLINE] DOI: https://doi.org/10.1112/jlms/jdn051
Strength of convergence and multiplicities in the spectrum of a C*-dynamical system
2008 - Published
Archbold, R. J., an Huef, A.
Proceedings of the London Mathematical Society, vol. 96, no. 3, pp. 545-581
Contributions to Journals: Articles
- [ONLINE] DOI: https://doi.org/10.1112/plms/pdm038
Limit sets and strengths of convergence for sequences in the duals of thread-like Lie goups
2007 - Published
Archbold, R. J., Ludwig, J., Schlichting, G.
Mathematische Zeitschrift, vol. 255, no. 2, pp. 245-282
Contributions to Journals: Articles
- [ONLINE] DOI: https://doi.org/10.1007/s00209-006-0023-1
Measuring noncommutativity in C*-algebras
2007 - Published
Archbold, R. J., Somerset, D. W. B.
Journal of Functional Analysis, vol. 242, no. 1, pp. 247-271
Contributions to Journals: Articles
- [ONLINE] DOI: https://doi.org/10.1016/j.jfa.2006.06.012
Strength of convergence in the orbit space of a transformation group
2006 - Published
Archbold, R. J., an Huef, A.
Journal of Functional Analysis, vol. 235, pp. 90-121
Contributions to Journals: Articles
- [ONLINE] DOI: https://doi.org/10.1016/j.jfa.2005.10.001
Stable rank and real rank of compact transformation group C*-algebras
2006 - Published
Archbold, R. J., Kaniuth, E.
Studia Mathematica, vol. 175, no. 2, pp. 103-120
Contributions to Journals: Articles
On the central Haagerup tensor product and completely bounded mappings of a C*-algebra
2005 - Published
Archbold, R. J., Somerset, D. W. B., Timoney, R. M.
Journal of Functional Analysis, vol. 226, no. 2, pp. 406-428
Contributions to Journals: Articles
- [ONLINE] DOI: https://doi.org/10.1016/j.jfa.2005.03.006

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External Memberships

Research Overview

Local variants of the Dixmier property and weak centrality for C*-algebras

The centre-quotient property and weak centrality for C^∗-algebras

Minimal primal ideals in the inner corona algebra of a C_{0}(X)-algebra

Maximally unitarily mixed states on a C*-algebra

Topological Frobenius reciprocity for representations of nilpotent groups and motion groups

The Dixmier property and tracial states for C*-algebras

The Inner Corona Algebra of a C0(X)-Algebra

Norms of inner derivations for multiplier algebras of C ∗ -algebras and group C ∗ -algebras, II

The C*-algebras of compact transformation groups

Minimal Primal Ideals in the Multiplier Algebra of a C₀(X)-algebra

Separation properties in the primitive ideal space of a multiplier algebra

Spectral synthesis in the multiplier algebra of a C_0(X)-algebra

Strength of convergence in non-free transformation groups

Ideals in the multiplier and corona algebras of a C_o(X)-algebra

Norms of inner derivations for multiplier algebras of C-algebras and group C-algebras

On the real rank of C*-algebras of nilpotent locally compact groups

Multiplier algebras of C_0(X)-algebras

Completely bounded mappings and simplicial complex structure in the primitive ideal space of a C^*-algebra

Factorial states, upper multiplicity and norms of elementary operators

Strength of convergence and multiplicities in the spectrum of a C*-dynamical system

Limit sets and strengths of convergence for sequences in the duals of thread-like Lie goups

Measuring noncommutativity in C*-algebras

Strength of convergence in the orbit space of a transformation group

Stable rank and real rank of compact transformation group C*-algebras

On the central Haagerup tensor product and completely bounded mappings of a C*-algebra

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Contributions to Journals