Prof. Gerard J. Murphy Department of Mathematics Sadly, Professor Gerard J. Murphy passed away in 2005.

He was an Associate Professor in the Mathematics Department of University College Cork (UCC) in Ireland. His research area was functional analysis. His principal interests were in the general theory of C*-algebras, the spectral and index theory of Toeplitz operators on Hardy spaces of ordered groups and bounded symmetric domains, and the C*-algebra approach to quantum groups . (A detailed account of his interests and the interests of his research group is available at the website of the UCC Operator Algebras Group.)

Royal Irish Academy: He was a member of the Publications Committee of the Royal Irish Academy and Editor-in-Chief of the Mathematical Proceedings of the Royal Irish Academy. This is a journal devoted to current research in all areas of pure mathematics and appears twice yearly. Original papers of good quality are sought. If you wish to submit a paper for publication, send it to the Publications Office of the Academy (19 Dawson Street, Dublin 2, Ireland). See the journal website for details on how to submit.

European Union Research Network: He was the Irish coordinator of the European Union Operator Algebras Network. This comprises a group of universities across seven countries in Europe that cooperate to promote research in operator algebras and noncommutative geometry. The Network supports postdoctoral fellowships at UCC and other universities of the research group.

Research Papers

The following is a list of most of his papers published since 1991.

• Ordered groups and crossed products of C*-algebras,
  Pacific J. Math. 148 (1991), 319--349.
• Derivations mapping into the radical,
  Arch. Math. 57 (1991), 469--474 (with M. Mathieu).
• Toeplitz operators and algebras,
  Math. Zeit. 208 (1991), 355--362.
• Spectral and index theory for Toeplitz operators,
  Proc. Royal Irish Acad. 91A (1991), 1--6.
• The analytic rank of a C*-algebra,
  Proc. Amer. Math. Soc. 115 (1992), 741--746.
• Almost-invertible Toeplitz operators and K-theory,
  J. Integr. Equ. Oper. Theory, 15 (1992), 72--81.
• The index group, the exponential spectrum and some spectral containment theorems,
  Proc. Royal Irish Acad. 92A (1992), 229--238.
• Toeplitz operators on generalised H^2 spaces,
  J. Integr. Equ. Oper. Theory, 15 (1992), 825--852.
• Inner functions and Toeplitz operators,
  Canadian Math. Bull. 36 (1993), 324--331.
• An index theorem for Toeplitz operators,
  J. Operator Theory 29 (1993), 97--114.
• Aspects of the theory of derivations,
  Funct. Anal. and Operator Theory 30 (1994), 267--275.
• Crossed products of C*-algebras by semigroups of automorphisms,
  Proc. London Math. Soc. (3) 68 (1994), 423--448.
• Fredholm index theory and the trace,
  Proc. Royal Irish Acad. 94A (1994), 161--166.
• Translation-invariant function algebras on compact abelian groups,
  Ann. Acad. Sci. Fennicae 20A (1995), 175--178.
• C*-algebras generated by commuting isometries,
  Rocky Mountain J. Math. 26 (1996), 237--267.
• C*-algebras with the approximate positive factorisation property,
  Trans. Amer. Math. Soc. (6) 348 (1996), 2291--2306 (with N.C. Phillips).
• Crossed products of C*-algebras by endomorphisms,
  J. Integr. Equ. Oper. Theory, 24 (1996), 298--319.
• Extensions of multipliers and dilations of projective isometric representations,
  Proc. Amer. Math. Soc., 125 (1997), 121--127.
• Type I Toeplitz algebras,
  J. Integr. Equ. Oper. Theory, 27 (1997), 221--227.
• Products of Toeplitz operators,
  J. Integr. Equ. Oper. Theory, 27 (1997), 439--445.
• Positive definite kernels and Hilbert C*-modules,
  Proc. Edinburgh Math. Soc., 40 (1997), 367--374.
• Averaging theorems for linear operators in compact groups and semigroups,
  Studia Math., 124 (1997), 249--258 (with T.T. West).
• Products of positive operators,
  Proc. Amer. Math. Soc., 125 (1997), 3675-3677.
• Compact topological semigroups,
  Proc. Royal Irish Acad., 97A (1997), 131--137 (with K. Abodayeh).
• Unitarily-invariant linear spaces in C*-algebras,
  Proc. Amer. Math. Soc., 126 (1998), 3597--3605 (with L.W. Marcoux).
• Invariant ideals in Toeplitz algebras,
  J. Integr. Equ. Oper. Theory, 35 (1999), 118--121.
• Uniqueness of the trace and simplicity,
  Proc. Amer. Math. Soc., 28 (2000), 3563--3570.
• Co-amenability of compact quantum groups,
  J. Geom. and Physics, 40 (2001), 129--153 (with E. Bedos and L. Tuset).
• Translation-invariant function algebras on compact groups,
  Adv. Stud. Contemp. Math., 3 (2001), 39--42.
• Simplicity of crossed products by endomorphisms,
  J. Integr. Equ. Oper. Theory, 42 (2002), 90--98.
• Amenability and co-amenability of algebraic quantum groups,
  Int. J. Math. & Math. Sci., 31 (2002), 577--601 (with E. Bedos and L. Tuset).
• Differential calculi over compact quantum groups and twisted cyclic co-cycles,
  J. Geom. Physics, 44 (2003), 570--594 (with J. Kustermans and L. Tuset).
• Toeplitz operators associated to unimodular algebras,
  J. Integr. Equ. Oper. Theory 46 (2003), 363--375. [PDF file]
• Amenability and co-amenability of algebraic quantum groups II,
  J. Funct. Anal. 201 (2003), 303--340 (with J. Kustermans and L. Tuset).
• Differential calculi over quantum groups
  Noncommutative Geometry and Quantum Groups
  Banach Centre Publ. 61 (2003), 157--170.
• Primitivity conditions for the full group C*-algebras,
  Bull. London Math. Soc. 35 (2003), 697--705. [PDF file]
• The C*-algebra of a function algebra,
  J. Integr. Equ. Oper. Theory 47 (2003), 361--374. [PDF file]
• Aspects of compact quantum group theory,
  Proc. Amer. Math. Soc. 132 (2004), 3055--3067 (with L. Tuset).
• The index theory associated to a non-finite trace on a C*-algebra,
  Canadian Math. Bull. 48 (2005), 252--259. [PDF file]
• Quantum groups, differential calculi and the eigenvalues of the Laplacian,
  Trans. Amer. Math. Soc. 357 (2005), 4681--4717 (with J. Kustermans and L. Tuset).
• Topological and analytical indices in C*-algebras,
  J. Funct. Anal. (to appear). [PDF file]

UCC School of Mathematics