UCD Research: Mathematical Sciences

People

Dr Michael Mackey BSc MSC PhD

Contact Details

Address	School of Mathematical Sciences Room 3.37 Radio House Belfield Office Park 10 Dublin 4
Telephone:	+353 1 716 2587
Email:	ei · dcu © yekcam · leahcim

Biography:

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.

Peer Reviewed Journals

Hoffmann, Philipp and Mackey, Michael and Ó Searcóid, Mícheál; (2011) 'On the second parameter of an $(m,p)$-isometry'. Integral Equations and Operator Theory, 71 :389-405. [Details]

Mackey, Michael; (2009) 'Homotopes of $\rm JB^*$-triples and a Russo-Dye theorem'. Asian-Eur. J. Math, 2 (3):465-475.

[DOI] [Details]

H\"ugli, Remo V. and Mackey, Michael; (2009) 'Transitivity of inner automorphisms in infinite dimensional Cartan factors'. Math. Z, 262 (1):125-141.

[DOI] [Details]

Dineen, Se\'an and Mackey, Michael; (2006) 'Confined Banach spaces'. Arch. Math. (Basel), 87 (3):227-232.

[DOI] [Details]

Mackey, Michael and Sevilla-Peris, Pablo and Vallejo, Jos\'e A.; (2006) 'Composition operators on weighted spaces of holomorphic functions on $JB^\ast$-triples'. Lett. Math. Phys, 76 (1):19-26.

[DOI] [Details]

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Associations

Association: Irish Mathematical Society, Function/Role: Committee member

Association: American Mathematical Society, Function/Role: Member

Conference Contributions

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 : UCD School of Mathematical Sciences Executive

Committee : UCD EMPS IT committee

Employment

Employer: UCD
Position: College Lecturer

Other Activities

Research Funding

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

Teaching Interests

Recent Postgraduates

Modules Taught

201000 MATH20260 Mathematics: The Mathematics of Google

201000 MATH30020 Mathematics: Algorithms

201000 MATH10230 Mathematics: Mathematics for Agriculture I

201000 MATH20270 Mathematics: Theory of Games

200800 MATH40020 Mathematics: Numerical Analysis

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Chu, Cho-Ho and Mackey, Michael; (2005) 'Isometries between $\rm JB^$-triples'. Math. Z*, 251 (3):615-633. [DOI] [Details]
Chu, C.-H. and H\"ugli, R. V. and Mackey, M.; (2004) 'The identity is isolated among composition operators'. Proc. Amer. Math. Soc, 132 (11):3305-3308. [DOI] [Details]
Mackey, M. and Mellon, P.; (2004) 'A Schwarz lemma and composition operators'. Integral Equations Operator Theory, 48 (4):511-524. [DOI] [Details]
Mackey, M. and Mellon, P.; (2003) 'Angular derivatives on bounded symmetric domains'. Israel J. Math, 138 :291-315. [DOI] [Details]
Isidro, Jos\'e M. and Mackey, Michael; (2002) 'The manifold of finite rank projections in the algebra $\scr L(H)$ of bounded linear operators'. Expo. Math, 20 (2):97-116. [DOI] [Details]
Mackey, M. and Mellon, P.; (2002) 'On an angular derivative result of Fan'. Math. Proc. R. Ir. Acad, 102A (1):115-126. [DOI] [Details]
Mackey, M. and Mellon, P.; (2001) 'Compact-like manifolds associated to $\rm JB^$-triples'. Manuscripta Math*, 106 (2):203-212. [DOI] [Details]
Dineen, Se\'an and Mackey, Michael and Mellon, Pauline; (1999) 'The density property for $JB^$-triples'. Studia Math*, 137 (2):143-160. [Details]
Mackey, M. and Mellon, P.; (1999) 'The quasi-invertible manifold of a $\rm JB^\ast$-triple'. Extracta Math, 14 (1):51-55. [Details]
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