A COMPLETE LIST OF MY PUBLICATIONS


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]


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, 301312.

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 operatorsstill not elementary?
Opuscula Mathematica 36 (2016), 787–797.

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).
 

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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