Gerard Murphy (mathematician) facts for kids

Gerard J. Murphy, a brilliant Irish mathematician.

Gerard J. Murphy (born November 1948 – died 12 October 2006) was a brilliant Irish mathematician. He wrote many famous textbooks that were used all over the world and translated into different languages. He passed away in October 2006, at 57 years old.

Gerard Murphy's Research

Gerard Murphy was a mathematician who studied complex ideas. His main area of research was called functional analysis. This is a branch of mathematics that looks at functions and spaces.

What He Studied

Later in his career, Gerard focused on quantum groups and non-commutative geometry. These are advanced topics that are important for both mathematics and physics. He wrote over 70 original math papers, sometimes by himself and sometimes with other mathematicians.

His Famous Book

He is also well-known for his book, C*-algebras and Operator Theory. This book was published in 1990 and became very popular around the world. It helped many students and researchers learn about these complex math ideas.

Important Groups and Networks

Gerard Murphy was involved in several important groups that helped advance mathematics.

Royal Irish Academy

He was a member of the Royal Irish Academy, which is a leading group for experts in Ireland. He also helped manage their publications and was the Editor-in-Chief for their math journal. This journal shares new research in pure mathematics twice a year.

European Union Research Network

Gerard was also the Irish leader for the European Union Operator Algebras Network. This group connects universities across seven European countries. They work together to support research in operator algebras and noncommutative geometry.

What People Said About Gerard

Many people admired Gerard Murphy's work and his dedication to teaching.

A Lasting Impact

Associate Professor Des MacHale from University College Cork said: "Gerard Murphy, like famous mathematicians before him, found new mathematical truths. These truths will last forever. Future students and researchers will build on his work."

His Dedication to Teaching

Professor Finbarr Holland, also from University College Cork, shared: "He always took his teaching seriously. He wanted students to understand and enjoy mathematics. He saw math not just as a tool, but as one of humanity's greatest achievements. He always worked to keep high academic standards."

Gerard Murphy's Life Story

Gerard Murphy was born in Drimnagh, Dublin, to May and Larry Murphy. He grew up in a large family with three boys and five girls.

Early Life and Education

Gerard left school when he was 14 years old. He worked in different simple jobs. But he never stopped learning. He taught himself at home with great focus and determination.

University Success

His hard work paid off. He got into Trinity College, Dublin, after doing well in a special course. In 1970, he started studying pure mathematics at Trinity. He was such a brilliant student that he won a special scholarship to help him with his studies.

In 1974, he graduated with top honors and won the Berkeley Gold Medal. His success at Trinity showed he was truly special. He then received the Gulbenkian Scholarship to study for his PhD at Cambridge University. He earned his PhD in 1977 and won the Knight Prize for his excellent research.

His Career as a Lecturer

After Cambridge, Gerard returned to Trinity College in 1977. He worked as a research fellow and began his career as a university lecturer. He then spent four years in North America, teaching at Dalhousie University, University of New Hampshire, and University of Oregon.

He was later appointed as a lecturer at University College Cork (UCC). He stayed there for the rest of his life. He was promoted quickly to associate professor. This was because of his high-quality research, great teaching, and contributions to the college.

Leading Research and Conferences

In the mid-1990s, Gerard was invited to join the EU Operator Algebras Network. His involvement helped him get a lot of funding from the EU. This money allowed him to organize major conferences on Operator Algebras at UCC. The first one was in 1995, bringing mathematicians from all over the world.

He also used the funding to support several research assistants. His work with this network helped create a top-level research center at UCC. This center focused on operator algebras and non-commutative geometry, leaving a lasting impact.

Head of Department and Later Years

In 1999, Gerard became the head of the Mathematics Department at University College Cork. He held this position for five years. He was very proud of being a member of the Royal Irish Academy. As an editor for their math journal, he helped modernize it and make it available online. He also helped raise its international profile.

In 2005, Gerard was diagnosed with cancer. He passed away peacefully at 57 years old. He is remembered by his wife Mary, his son, three daughters, his mother, and his siblings.

Remembering Gerard Murphy

Professor Richard Timoney of Trinity College Dublin wrote about Gerard Murphy in a book. He mentioned that Gerard came from a working-class background and did not have a typical high school education. However, he caught the attention of the School of Mathematics at Trinity.

Mentorship and Collaboration

Trevor West, another mathematician, took a special interest in Gerard. He was pleased to see Gerard become a very good math student. Gerard later did his PhD at Cambridge and then returned to Trinity for a research fellowship. He worked productively with Trevor West there.

After some time in North America, Gerard was appointed in Cork. This meant he was still close to Trevor West. Trevor encouraged Gerard to organize international research meetings in Cork, and Gerard did so many times.

Important Mathematical Work

Gerard Murphy and Trevor West wrote several papers together. One important paper, published in 1979, included a very elegant formula for something called the spectral radius in C*-algebras.

Gerard was also elected to the Royal Irish Academy and became an editor of its math journal. These achievements were likely supported by Trevor West, who often promoted Gerard's great abilities.

The "Little Red Book"

One of their most notable joint efforts was a math book published in 1982. It was a team effort with four authors: Bruce Barnes, Gerard Murphy, Roger Smyth, and Trevor West. This book, often called 'the little red book', still has lasting value. It contains definitions and ideas that are still useful today and might not be found elsewhere.

Roger Smyth, one of the co-authors, said that Trevor West was the main person behind the book. Trevor was very involved, even deciding to rewrite a large part of the book late in the process to make it clearer.

Gerard's Contribution to Explaining Math

Gerard Murphy might have contributed to the book by being very good at explaining complex ideas. Later, in 1990, Gerard published his own book called C*-algebras and Operator Theory. This book became a standard reference. It covers the basics of the theory and also touches on more advanced topics. Many new students still find it a valuable introduction to C*-algebras.

This remembrance was added by Carol Murphy, Gerard's sister, with permission from Dr. Timoney and Maura Lee West.

Selected Publications

Gerard Murphy wrote many important mathematical papers. Here are some of his publications from 1991 onwards:

• 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, Canad. 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. Analysis 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.
• Amenability and co-amenability of algebraic quantum groups II, J. Funct. Analysis 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.
• The C*-algebra of a function algebra, J. Integr. Equ. Oper. Theory 47 (2003), 361–374.
• 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, Canad. Math. Bull. 48 (2005), 252–259.
• 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. Analysis (234) 2006, 261–276.