Internal/Preliminary
Reports:

On the spectrum of multiplications on von
Neumann algebras,

Sem. Ber. Funkt. Anal. SS 1982, Tübingen 1982,
113–122.

A remark on elementary operators,

Sem. Ber.
Funkt. Anal. WS 1983/84, Tübingen 1984, 239–247.

On weakly
compact elementary operators,

Sem. Ber. Funkt. Anal. WS 1984/85,
Tübingen 1985, 177–185.

A short geometric proof of Archbold's
characterization of prime C*-algebras as antilattices,

Sem. Ber.
Funkt. Anal. WS 1985/86, Tübingen 1986, 101–104.

On
approximate point spectra of elementary operators,

Sem. Ber.
Funkt. Anal. WS 1985/86, Tübingen 1986, 105–116.

Generalising
elementary operators,

Sem. Ber. Funkt. Anal. SS 1988, Tübingen
1988, 133–153.

Primitive Banach algebras need not be
ultraprime,

Sem. Ber. Funkt. Anal. SS 1989, Tübingen 1989,
5–9 (with P. Ara).

On C*-algebras of quotients,

Sem.
Ber. Funkt. Anal. SS 1989, Tübingen 1989, 107–120.

Is there
an unbounded Kleinecke–Shirokov theorem?

Sem. Ber. Funkt. Anal.
SS 1990, Tübingen 1990, 137–143.

**Doctoral
Thesis:**

Applications of ultraprime Banach algebras
in the theory of elementary operators, Tübingen,
1986.

**Research Papers:**

Spectral
theory for multiplication operators on C*-algebras,

Proc. Roy.
Irish Acad. 83A (1983), 231–249.

A characterization of
positive multiplications on C*-algebras,

Math. Japon. 29
(1984), 375–382.

Enlargements of almost open
mappings,

Proc. Amer. Math. Soc. 96 (1986), 247–248 (with
R. E. Harte).

Elementary operators on prime C*-algebras,
I,

Math. Ann. 284 (1989), 223–244.

Elementary operators on
prime C*-algebras, II,

Glasgow Math. J. 30 (1988),
275–284.

Compact and weakly compact multiplications on
C*-algebras,

Ann. Acad. Sci. Fenn. Ser. A. I. Math. 14
(1989), 57–62.

Properties of the product of two derivations
of a C*-algebra,

Canad. Math. Bull. 32 (1989),
490–497.

Rings of quotients of ultraprime Banach algebras.
With applications to elementary operators,

Proc. Centre Math.
Anal. Austral. Nat. Univ. 21 (1989), 297–317.

Weakly compact
homomorphisms from C*-algebras are of finite rank,

Proc. Amer.
Math. Soc.107 (1989), 761–762.

More properties of the product of two
derivations of a C*-algebra,

Bull. Austral. Math. Soc. 42 (1990),
115–120.

The symmetric algebra of quotients of an ultraprime
Banach algebra,

J. Austral. Math. Soc. 50 (1991),
75–87.

On ultraprime Banach algebras with non–zero
socle,

Proc. Roy. Irish Acad. 91A (1991), 89–98 (with P.
Ara).

Derivations mapping into the radical,

Arch. Math. 57
(1991), 469–474 (with G. J. Murphy).

A local version of
the Dauns–Hofmann theorem,

Math. Z. 208 (1991), 349–353 (with P. Ara).

Posner's second theorem deduced from the
first,

Proc. Amer. Math. Soc. 114 (1992),
601–602.

Derivations mapping into the radical, II,

Bull.
London Math. Soc. 24 (1992), 485–487 (with V.
Runde).

Uniqueness of a Lindblad decomposition, in:
Elementary operators and applications,

Proc. Int. Workshop,
Blaubeuren, Germany, June 1991; World Scientific, Singapore, 1992,

179–187 (with Th. S. Freiberger).

An application of
local multipliers to centralizing mappings of C*-algebras,

Quart.
J. Math. Oxford (2) 44 (1993), 129–138 (with P.
Ara).

The cb–norm of a derivation, in: Algebraic
methods in operator theory,

R. E. Curto, P. E. T. Jørgensen
(eds.), Birkhäuser, Basel – Boston, 1994, 144–152.

On the
central Haagerup tensor product,

Proc. Edinburgh Math. Soc. 37
(1994), 161–174 (with P. Ara).

On the range of
centralizing derivations,

Contemp. Math. 184 (1995),
291–297.

Spectrally bounded generalized inner
derivations,

Proc. Amer. Math. Soc. 123 (1995), 2431–2434 (with R. E. Curto).

Derivations mapping into the radical,
III,

J. Funct. Anal. 133 (1995), 21–29 (with M.
Bresar).

Commutativity preserving mappings on semiprime
rings,

Commun. Algebra 25 (1997), 247–265 (with R.
Banning).

Derivations implemented by local
multipliers,

Proc. Amer. Math. Soc. 126 (1998),
1133–1138.

Characterising completely positive elementary
operators,

Bull. London Math. Soc. 30 (1998), 603–610.

A
simple local multiplier algebra,

Math. Proc. Cambridge Phil.
Soc. 126 (1999), 555–564 (with P. Ara).

Elementary
operators on antiliminal C*-algebras,

Math. Ann. 313
(1999), 609–616 (with R. J. Archbold and D. W. B.
Somerset).

The continuity of Lie
homomorphisms,

Studia Math. 138 (2000), 193–199 (with B.
Aupetit).

First results on spectrally bounded
operators,

Studia Math. 152 (2002), 187–199 (with G. J.
Schick).

Spectrally bounded operators from von Neumann
algebras,

J. Operator Th. 49 (2003), 285–293 (with G. J.
Schick).

The structure of Lie derivations on C*-algebras,

J. Funct.
Anal. 202 (2003), 504–525 (with A. R. Villena).

Spectrally bounded traces on C*-algebras,

Bull. Austral. Math.
Soc. 68 (2003), 169–173.

Spectrally bounded operators on
simple C*-algebras,

Proc. Amer. Math. Soc. 132 (2004), 443–446.

Spectrally bounded operators on simple C*-algebras II, [pdf]

Irish Math. Soc. Bull. 54 (2004), 33–40.

Symmetric amenability and Lie derivations,

Math. Proc.
Cambridge Phil. Soc. 137 (2004), 433–439 (with J.
Alaminos and A. R. Villena).

Hereditary properties of spectral isometries,

Arch. Math. 82
(2004), 222–229 (with A. R. Sourour).

Commutators
with finite spectrum, [pdf]

Illinois J. Math. 48 (2004),
687–699 (with N. Boudi).

A not so simple local multiplier algebra,

J. Funct. Anal. 237
(2006), 721–737 (with P. Ara).

Jordan isomorphism of purely infinite C*-algebras,

Quart. J.
Math. 58 (2007), 249–253 (with Y.-F. Lin).

Spectral isometries, II,

Contemp. Math. 435 (2007),
301–309 (with C. Ruddy).

The Weyl calculus: finite dimensional
aspects,

Math. Proc. R. Ir. Acad. 107A (2007), 171–181
(with W. J. Ricker).

Maximal C*-algebras of quotients and injective envelopes of
C*-algebras,

Houston J. Math. 34 (2008), 827–872 (with P.
Ara).

The maximal C*-algebra of quotients as an operator bimodule,

Arch. Math. 92 (2009), 405–413 (with P. Ara and E. Ortega) [pdf]

A collection of problems on spectrally bounded operators,

Asian-Eur. J. Math. 2 (2009), 489–503 [pdf]

Sheaves of C*-algebras,

Math. Nachrichten 283 (2010), 21–39 (with P. Ara).

Elementary operators that are spectrally bounded,

Operator Theory: Advances and Applications 212 (2011), 1–15 (with N. Boudi).

When is the second local multiplier algebra of a C*-algebra equal to the first?

Bull. London Math. Soc. 43 (2011), 1167–1180 (with P. Ara). [pdf]

C*-Segal algebras with order unit,

J. Math. Analysis Appl. 398 (2013), 785–797
(with J. Kauppi). [pdf]

Spectral isometries on non-simple C*-algebras,

Proc. Amer. Math. Soc. 142 (2014), 129–145 (with A. R. Sourour). [pdf]

Locally quasi-nilpotent elementary operators,

Operators & Matrices 8 (2014), 785–798 (with N. Boudi).

More elementary operators that are spectrally bounded,

J. Math. Analysis Appl. 428 (2015), 471–489 (with N. Boudi). [pdf]

Spectral isometries into commutative Banach algebras,

Contemp. Math. 645 (2015), 217–222 (with M. Young).
[pdf]

Spectrally isometric elementary operators,

Studia Math. 236 (2017), 33–49 (with M. Young). [online first]

Strictly singular multiplication operators on L(X),

Israel J. Math. 236 (2020), 685–709 (with P. Tradacete). [pdf]

Characterizing Jordan homomorphisms,

Acta Sci. Math. (Szeged) 86 (2020), 697–701. [pdf]

Exact structures for operator modules,

Canad. J. Math. 75 (2023), 421–446 (with M. Rosbotham). [pdf]

Schanuel's lemma for exact categories,

Complex Anal. Oper.Theory 16 (2022),
(with M. Rosbotham). [pdf]

Relative double commutants in coronas of separable C*-algebras,

Glasgow Math. J. (2022) (with D. Kucerovsky) [online first].

Invertibility preserving mappings onto finite C*-algebras,

Studia Math., to appear (with F. Schulz). [pdf]

On the range of TRO-conditional expectations,

Linear Alg. Appl. 670 (2023), 78–103 (with Y. Estaremi).

**Historical Papers:**

On the origin of
the notion 'ergodic theory',

Expo. Math. 6 (1988),
373–377.

**Expository Papers:**

How to use
primeness to describe properties of elementary operators,

Proc.
Sympos. Pure Math. 51 (1990), Part 2, 195–199.

Derivations
and completely bounded maps on C*-algebras. A survey,

Irish Math.
Soc. Bull. 26 (1991), 17–41.

How to solve an operator
equation,

Publ. Mat. 36 (1992), 743–760.

Where to find the
image of a derivation,

Banach Center Publ. 30 (1994),
237–249.

Operator equations with elementary
operators,

Contemp. Math. 185 (1995), 259–272.

Advances
towards the non–commutative Singer–Wermer theorem?

CRM preprint
series 314 (1995).

Representation
theorems for some classes of operators on C*-algebras, [ps]

Irish
Math. Soc. Bull. 41 (1998), 44–56.

Ten years
of local multipliers, [ps]

Irish Math. Soc. Bull. 43 (1999),
64–69.

Lie mappings of C*-algebras,

in Nonassociative
Algebra and its Applications, R. Costa et al (eds.), Marcel Dekker,

New York 2000, 229–234.

The norm problem for elementary
operators,

in Recent Progress in Functional Analysis, K. D.
Bierstedt et al (eds.), North–Holland Math. Studies
189,

Elsevier, Amsterdam 2001, 363–368.

Elementary
operators on Calkin algebras, [pdf]

Irish Math. Soc. Bull. 46
(2001), 33–42.

Another automatic boundedness technique,

Contemp. Math. 363
(2004), 241–248.

What is non–commutative Functional Analysis about?

The Irish
Scientist Year Book, Oldbury Publ., Dublin 2004, p. 86.

Spectral isometries,

Proc. Conf. in honour of Prof. W.
Zelazko's 70th birthday,

(Bedlewo, 11–17 May 2003), Banach Center
Publ. 67 (2005), 265–269.

Towards a non-selfadjoint version of
Kadison's theorem,

Proc. Conf. in honour of L. Fejér's and F.
Riesz's 125th birthday,

(Eger, 9-13 June 2005); Ann. Math. Inf.
32 (2005), 87–94.

The local multiplier algebra:
blending noncommutative ring theory and functional
analysis,

Proc. Conf. on Modules & Comodules (Porto, 8-10
September 2006); Birkhauser Verlag,

Basel, 2008, 301–312.

The second local multiplier algebra of a separable C*-algebra,

in Proc. Conf. on Operator Theory and its Applications, in honour of Victor Shulman's 65th birthday,

(Gothenburg, 26-29 April 2011); Operator Theory: Advances and Applications 233 (2013), 93–102. [pdf]

Interplay between spectrally bounded operators and Complex Analysis,

Irish Math. Soc. Bull. 72 (2013), 57–70. [pdf]

A brief history of the Irish Mathematical Society,

EMS Newsletter 94 (2014),
50–51.

Elementary operators–still not elementary?

Opuscula Mathematica 36 (2016), 787–797.

Towards a sheaf cohomology theory for C*-algebras,

in: Banach Algebras and Applications, Oulu, 2017, de Gruyter, 2020.

Injectivity,

Irish Math. Soc. Bull. 85 (2020), 31–44 (with M. Rosbotham).
[pdf]

**Books, Editorial Work, etc.**

Proc.
Int. Workshop on Elementary Operators and Applications
(ed.),

(Blaubeuren, June 9–12, 1991), World Scientific,
Singapore, 1992.

Proc. 13th Int. Conference on Banach
Algebras 1997 (ed.),

(Blaubeuren, July 20–August 3, 1997), Walter
de Gruyter, Berlin, 1998 (with E.
Albrecht).

Funktionalanalysis. Ein Arbeitsbuch,

Spektrum
Akademischer Verlag, Heidelberg–Berlin–Oxford, 1998.

Local
Multipliers of C*-algebras, [link]

Springer–Verlag, London, 2003
(with P. Ara).

Proc.
All Ireland Algebra Days 2001 (ed.), [link]

(Belfast, 16–19 May
2001), Irish Math. Soc., Belfast, 2003.

Proc. 3rd Int. Workshop on Elementary Operators and their Applications (ed.), [link]

(Belfast, April 14–17, 2009); Operator Theory: Advances and Applications 212, Birkhauser Verlag, Basel, 2011 (with R. E. Curto).

Classically Semisimple Rings. A Perspective Through Modules and Categories.

Springer–Verlag, Heidelberg, December 2022.

**Book Reviews**

"Lectures on amenability'' by V. Runde,

Math. Reviews,
MR2003h:46001, Amer. Math. Soc. (2003), 3pp.

"Completely bounded maps and operator algebras'' by V.
Paulsen,

Bull. London Math. Soc. 36 (2004), 711–713.

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