Navigation

Researchers at UCD

researcher

Michael Mackey

Lecturer In Mathematics

School of Mathematics & Statistics
SCN 104B
UCD Belfield
Dublin 4
map
PGP public key

Tel: +353 1 716 2587
Email: mackey © maths · ucd · ie

Professional

 

Associations

Association: Irish Mathematical Society, Function/Role: President 2015/16
Association: Irish Mathematical Society, Function/Role: Vice President 2013/14
     

Conference Contributions

Mackey, M. (2014) [Conference Organising Committee Member], Jordan Geometric Analysis and Applications, Queen Mary, Uinversity of London , 03-SEP-14 - 05-SEP-14.
M. Mackey (2012) International conference on Jordan Theory and related topics in celebration of the 65th birthday of Professor Cho-Ho Chu webpage. [Invited Oral Presentation], Jordan Theory and Related Topics, Hong Kong , 30-APR-12 - 04-MAY-12.
Mackey, M.; (2009) A four day meeting on Complex Analysis on Infinite Dimensional Spaces marking the retirement of Professor Sean Dineen from the UCD School of Mathematical Sciences. [Conference Organising Committee Member], Complex Analysis on Infinite Dimensional Spaces, University College Dublin , 23-JUN-09 - 26-AUG-09.
Mackey, M.; (2008) A two day meeting on Jordan algebraic structures in analysis and geometry. [Conference Organising Committee Member], Jordan structures: nonassociative analysis and geometry, School of Mathematical Sciences at Queen Mary college, University of London , 05-SEP-08 - 06-SEP-08.
Mackey, M.; (2005) Composition Operators on Bounded Symmetric Domains. [Invited Lecture], Infinite Dimensional Analysis, Kent State University, Ohio, USA , 09-FEB-05 - 13-FEB-05.
Mackey, M.; (2006) Invited speaker : Confined Banach Spaces. [Invited Lecture], Workshop on Jordan Structures in analysis and geometry, Kaohsiung, Taiwan , 03-APR-06 - 07-APR-06.

Committees

Committee : Irish Mathematical Society

Employment

Employer: UCD
Position: College Lecturer
         

Other Activities

Research Funding

  • 2005-2007 R. Hugli and M. Mackey, IRCSET postdoctoral fellowship, €90,000

Publications

     

Peer Reviewed Journals

M. Mackey and W. G. Sullivan (2017) 'Exhaustion of an interval by iterated Rényi parking'. Journal of Mathematical Analysis and Applications, 446 (1):38-61. [DOI] Link to full text [Details]
P. Hoffmann, M. Mackey (2015) '(m,p)-isometric and (m,infinity)-isometric operator tuples on normed spaces'. Asian-European Journal of Mathematics, 8 (2). [DOI] Link to full text [Details]
Mackey, M. (2013) 'Local derivations on Jordan triples'. Bulletin of the London Mathematical Society, 45 (4):811-824. [DOI] Link to full text [Details]
Philipp Hoffmann, Michael Mackey and Mícheál Ó Searcóid (2011) 'On the second parameter of an (m,p)-isometry'. Integral Equations and Operator Theory, 71 (3):389-405. [DOI] Link to full text [Details]
Mackey, Michael (2009) 'Homotopes of JB*-triples and a Russo-Dye theorem'. Asian-European Journal of Mathematics, 2 (3):465-475. Available Online [DOI] Link to full text [Details]
Hügli, Remo V. and Mackey, Michael (2009) 'Transitivity of inner automorphisms in infinite dimensional Cartan factors'. Mathematische Zeitschrift, 262 (1):125-141. Available Online [DOI] Link to full text [Details]
Dineen, Seán and Mackey, Michael (2006) 'Confined Banach spaces'. Archiv der Mathematik, 87 (3):227-232. Available Online [DOI] [Details]
Mackey, Michael and Sevilla-Peris, Pablo and Vallejo, José A.; (2006) 'Composition operators on weighted spaces of holomorphic functions on JB*-triples'. Letters in Mathematical Physics, 76 (1):19-26. Available Online [DOI] [Details]
Chu, Cho-Ho and Mackey, Michael (2005) 'Isometries between JB*-triples'. Mathematische Zeitschrift, 251 (3):615-633. Available Online [DOI] [Details]
Chu, C.-H. and Hügli, R. V. and Mackey, M. (2004) 'The identity is isolated among composition operators'. Proceedings of the American Mathematical Society, 132 (11):3305-3308. Available Online [DOI] Link to full text [Details]
Mackey, M. and Mellon, P.; (2004) 'A Schwarz lemma and composition operators'. Integral Equations Operator Theory, 48 (4):511-524. Available Online [DOI] Link to full text [Details]
Mackey, M. and Mellon, P.; (2003) 'Angular derivatives on bounded symmetric domains'. Israel J. Math, 138 :291-315. Available Online [DOI] Link to full text [Details]
Isidro, José M. and Mackey, Michael (2002) 'The manifold of finite rank projections in the algebra L(H) of bounded linear operators'. Expositiones Mathematicae, 20 (2):97-116. Available Online [DOI] [Details]
Mackey, M. and Mellon, P.; (2002) 'On an angular derivative result of Fan'. Math. Proc. R. Ir. Acad, 102A (1):115-126. Available Online [DOI] [Details]
Mackey, M. and Mellon, P. (2001) 'Compact-like manifolds associated to JB*-triples'. Manuscripta Mathematica, 106 (2):203-212. Available Online [DOI] [Details]
Michael Mackey (2000) 'The Grassmannian manifold associated to a bounded symmetric domain'. Lecture Notes in Pure and Applied Mathematics, 214 :317-323. [Details]
Dineen, Seán and Mackey, Michael and Mellon, Pauline (1999) 'The density property for JB*-triples'. Studia Mathematica, 137 (2):143-160. [Details]
Mackey, M. and Mellon, P. (1999) 'The quasi-invertible manifold of a JB*-triple'. Extracta Mathematicae, 14 (1):51-55. [Details]
   

Published Reports

Michael Mackey (2015) Irish Mathematical Society President's Report. Irish Mathematical Society, Kildare. Available Online [Details]
Michael Mackey (2016) Irish Mathematical Society President's Report. Irish Mathematical Society, Kildare. Available Online [Details]
                         

Translation

M. Maestre, A. Galbis (2012) Vector Analysis vs Vector Calculus. Springer, New York: Translation [Details]
                                                                                   

Research

Research Interests

I'm mainly interested in Jordan structures (especially JB*-triples) which means knowing something of functional analysis, complex analysis, non-associative algebras and calculus of manifolds.

Let me give a short explanation of what a JB*-triple is by way of example. Everybody (?) knows that the square matrices of size n form an algebra, that is, a vector space where one can add and multiply any two elements, and the associative law holds. If we symmetrise the product by
A o B = (AB+BA)/2
then we get a different algebra- one which is commutative but not associative. It is a typical example of a Jordan algebra. Now consider non-square matrices, take 2x3 matrices for example. You can't matrix multiply two of these and hope to get another of the same type. However if you take three such matrices then you can multiply them and get another 2x3 matrix (multiply by transposing the matrix in the centre to get a 3x2). So we have a triple structure. The associative law holds in the sense that (ABC)DE = A(BCD)E = AB(CDE). If we now symmetrise this triple product on the 2x3 matrices, to get
{A,B,C} = (ABC + CBA)/2
then we have a typical example of a Jordan triple. The metric stucture supplied by the usual matrix norm makes this algebraic structure into a JB* triple.


Research Projects

Sponsor : Irish Research Council for Science Engineering and Technology (IRCSET)
Title : Contractive projections and conditional expectations in operator algebrase
Start Date / End Date : 01-NOV-05 / 31-OCT-07

Recent Postgraduates

In 2013, Philipp Hoffmann completed  his Ph.D. on the topic of genralised isometries in Banach spaces under the supervision of Mícheál Ó Searcóid and myself.  Philipp currently works in NUI Maynooth.