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Rupert Levene

Lecturer

School of Mathematics & Statistics
S3.06, Science Centre South
Belfield
Dublin 4

Tel: +353 1 716 2558
Email: rupert.levene@ucd.ie

Biography

My research interests are in operator algebras, operator spaces and quantum information theory.

Select "Research" and "Publications" for more information.

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Professional

 

Associations

Association: Irish Mathematical Society, Function/Role: Committee member
Association: Irish Mathematical Society, Function/Role: Member
Association: London Mathematical Society, Function/Role: Member
Association: European Mathematical Society, Function/Role: Member
     

Conference Contributions

Kribs DW; Levene, RH; Power SC (2017) Weighted shift directed graph operator algebras. [Invited Lecture], Queen's University Belfast Pure Mathematics Colloquium, Belfast , 03-MAR-17 - 03-MAR-17.
Crann, JC; Kribs DW; Levene RH; Todorov IG (2016) An infinite-dimensional approach to privacy and complementarity. [Invited Lecture], Workshop on Representation Theory in Quantum Information, University of Guelph, Canada , 22-AUG-16 - 25-AUG-16.
Kribs DW; Levene, RH; Power SC (2016) Weighted shift directed graph operator algebras. [Invited Lecture], University of Glasgow Analysis Seminar, Glasgow, UK , 01-NOV-16 - 01-NOV-16.
Kribs DW; Levene, RH; Power SC (2016) Weighted shift directed graph operator algebras. [Invited Lecture], University of Newcastle Analysis Seminar, Newcastle, UK , 06-DEC-16 - 06-DEC-16.
Eleftherakis, GK; Levene, RH; Todorov IG (2015) The Boolean lattice of Schur idempotents. [Invited Lecture], Annual meeting of the Irish Mathematical Society, University College Cork , 27-AUG-15 - 28-AUG-15.
Eleftherakis, GK; Levene, RH; Todorov IG (2015) The Boolean lattice of Schur idempotents. [Invited Lecture], Infinite Dimensional Function Theory: Present Progress and Future Problems, UCD , 08-JAN-15 - 09-JAN-15.
Eleftherakis, GK; Levene, RH; Todorov IG (2015) Schur idempotents and hyperreflexivity. [Oral Presentation], Banach Algebras and their Applications, Fields Institute, Toronto , 04-AUG-15 - 12-AUG-15.
   

Education

Year 2000 Institution: University of Cambridge
Qualification: BA Subject: BA Hons, Mathematics, Pure and Applied
Year 2004 Institution: Lancaster University. UK
Qualification: PhD Subject: PhD in Pure Mathematics
Year 2001 Institution: University of Cambridge
Qualification: Other Subject: Certificate of Advanced Study in Mathematics (Part III)
         

Publications

     

Peer Reviewed Journals

Levene, RH; Lin; Y-F; Todorov, IG (2017) 'Positive extensions of Schur multipliers'. Journal of Operator Theory, 78 (1):45-69. Available Online [DOI] [Details]
Kribs, DW; Levene, RH; Power, SC (2017) 'Commutants of weighted shift directed graph operator algebras'. Proceedings of the American Mathematical Society, 145 :3465-3480. Available Online [DOI] [Details]
Levene, RH; Spronk, N; Todorov, IG; Turowska, L (2016) 'Schur multipliers of Cartan pairs'. Proceedings of the Edinburgh Mathematical Society, :1-28. Available Online [DOI] [Details]
Eleftherakis, GK; Levene, RH; Todorov, IG (2016) 'Schur idempotents and hyperreflexivity'. Israel Journal of Mathematics, 215 :317-337. Available Online [DOI] [Details]
Levene, RH; Piszczek, K (2016) 'Grothendieck's inequality in the noncommutative Schwartz space'. Studia Mathematica, 234 (2):185-194. [DOI] [Details]
Timoney, RM; Levene, RH (2016) 'Corrigendum to Completely bounded norms of right module maps'. Linear Algebra and Its Applications, 505 :387-389. Available Online [DOI] [Details]
Crann, J; Kribs, DW; Levene, RH; Todorov, IG (2016) 'Private algebras in quantum information and infinite-dimensional complementarity'. Journal of Mathematical Physics, 57 (1). Available Online [DOI] [Details]
Rupert H. Levene (2014) 'Norms of idempotent Schur multipliers'. New York Journal of Mathematics, 20 :325-352. Available Online Link to full text [Details]
Levene, RH; Timoney, RM (2012) 'Completely bounded norms of right module maps'. Linear Algebra and Its Applications, 436 (5):1406-1424. Available Online [DOI] [Details]
Levene, RH; Power, SC (2009) 'Manifolds of Hilbert space projections'. Proceedings of the London Mathematical Society, 100 (2):485-509. [DOI] [Details]
Juschenko, K; Levene, RH; Todorov, IG; Turowska, L (2009) 'Compactness properties of operator multipliers'. Journal of Functional Analysis, 256 (11):3772-3805. [DOI] [Details]
Davidson, KR; Levene, RH; Marcoux LW; Radjavi H (2008) 'Erratum: On the topological stable rank of non-selfadjoint operator algebras'''. Mathematische Annalen, 341 (4):963-964. [DOI] [Details]
Davidson, KR; Levene, RH; Marcoux LW; Radjavi H (2008) 'On the topological stable rank of non-selfadjoint operator algebras'. Mathematische Annalen, 341 (2):239-253. [DOI] [Details]
Davdison, KR; Levene, RH (2006) '1-hyperreflexivity and complete hyperreflexivity'. Journal of Functional Analysis, 235 (2):666-701. [DOI] [Details]
Levene, RH (2006) 'A double triangle operator algebra from SL2(R+)'. Canadian Mathematics Bulletin, 49 (1):117-126. [Details]
Levene, RH; Power, SC (2003) 'Reflexivity of the translation-dilation algebra on L2(R)'. International Journal of Mathematics, 14 (10):1081-1090. [Details]
                                                                                                                     

Research

Research Interests

My research involves the study of operator algebras, operator spaces and quantum information theory. In particular, I am interested in:
  • Reflexivity and hyperreflexivity: a (non-selfadjoint) operator algebra is reflexive if, loosely speaking, it has a lot of invariant subspaces. It is hyperreflexive if the distance to the algebra can be estimated using its invariant subspaces; this is stronger than reflexivity. These properties have natural generalisations from operator algebras to operator spaces, and a key question is to try to determine which operator spaces are reflexive and which are hyperreflexive.
  • Completely bounded mappings between operator spaces and their norms: completely bounded mappings are at the heart of the theory of operator spaces. A linear map between operator spaces comes equipped with two natural norms: the operator norm, and the completely bounded norm. One fundamental problem is to determine when one of these two norms may be estimated using the other, or when they are equal.
  • Schur multipliers: these completely bounded mappings have many attractive properties; for example, their norm and completely bounded norm always agree. However, there are many interesting open questions about this class of mappings, such as: what are the possible values of the norm of an idempotent Schur multiplier?
  • Quantum information theory tackles problems of fundamental importance to the success of quantum computing, a technology still very much in its infancy. There turn out to be intimate connections with the theory of completely bounded maps. My work to date has focussed on privacy and correctability in the infinite dimensional setting.