Conference on Automatic Continuity and Banach


This volume contains papers and problems presented to the Conference on Automatic Continuity and Banach Algebras, held at the Australian National University, January 2 - 20, 1989. The timing and duration of this conference was designed to fit into the January break of many northern hemisphere universities, yet to have a workshop environment to enhance interaction between participants.

The articles are essentially expanded versions of the talks given at the conference, with the exception of several papers which are appearing elsewhere. By deliberate policy the papers herein contain historical background, syntheses and expository accounts, as well as the development of new ideas and results. Following the papers is a list of unsolved problems presented here at Canberra. This volume concludes with a progress report on the problem list of the Long Beach conference on Radical Banach Algebras and Automatic Continuity, 1981.

The participants would like to thank the Centre for Mathematical Analysis for hosting the conference and providing most of the financial support, the Australian Mathematical Society who supported the conference with a Special Interest Meeting grant, and the Mathematical Sciences Research Centre of the Faculty of Science, Australian National University, who funded the visit of N. Grønbæk. On a personal level, appreciation is expressed to Marilyn Gray, Joyce Heinz, Dorothy Nash and Jill Smith, who dealt with all the day to day queries and worries with total aplomb, as well as handling the typing of the papers for these proceedings.

I, myself, would like to thank all participants for making the conference such a success. Special thanks are due to Kjeld Laursen for organizing the conference problem sessions and collating the resulting material for inclusion here, and Niels Grønbæk and George Willis for their assistance in the editing of this volume.



Chapter Page number
1 - Power-bounded elements in a Banach algebra and a theorem of Gelfand (pdf 944.04 KB)
G.R. Allan
2 - Locally inner derivations (pdf 1.1 MB)
G.R. Allan
3 - The Wedderburn decomposition for quotient algebras arising from sets of non-synthesis (pdf 619.13 KB)
William G. Bade
4 - The Raikov convolution measure algebra (pdf 901.62 KB)
Gavin Brown and William Moran
5 - Banach algebra techniques and extensions of operator-valued representations (pdf 941.24 KB)
B. Chevreau and J. Galé
6 - Complementation problems concerning the radical of a commutative amenable Banach algebra (pdf 406.37 KB)
P.C. Curtis Jr.
7 - On norms on algebras (pdf 2.51 MB)
H.G. Dales
8 - Weak (F)-amenability of R(X) (pdf 1.45 MB)
J.F. Feinstein
9 - Banach algebras generated by analytic semigroups having compactness properties on vertical lines (pdf 1.57 MB)
José E. Galé
10 - Automorphisms of weighted measure algebras (pdf 902.28 KB)
F. Ghahramani
11 - Semigroups and the structure of weighted convolution algebras (pdf 1.51 MB)
Sandy Grabiner
12 - Using Banach algebras to do analysis with the umbral calculus (pdf 1.67 MB)
Sandy Grabiner
13 - Constructions preserving weak amenability (pdf 1.25 MB)
Niels Grønbæk
14 - Some remarks about ideas and results in topological homology (pdf 3.46 MB)
A.Ya. Helemskii
15 - Banach algebras occurring in spectral theory (pdf 1.22 MB)
Igor Kluvánek
16 - Intertwining with isometries (pdf 443.25 KB)
K.B. Laursen
17 - Some problems concerning reflexive operator algebras (pdf 1.22 MB)
W.E. Longstaff
18 - Remarks on semisimple reflexive algebras (pdf 1.28 MB)
W.E. Longstaff
19 - Subalgebras of amenable algebras (pdf 1.01 MB)
Richard J. Loy
20 - Rings of quotients of ultraprime Banach algebras, with applications to elementary operators (pdf 1.92 MB)
Martin Mathieu
21 - Derivations of convolution algebras (pdf 913.76 KB)
J.P. McClure
22 - Function theory on Banach algebras (pdf 440.13 KB)
R. Parvatham
23 - Factorization in group algebras (pdf 1.05 MB)
G.A. Willis
24 - Ultraprime group algebras (pdf 425.49 KB)
G.A. Willis
25 - The norms of powers of functions in the Volterra algebra, II (pdf 129.27 KB)
G.A. Willis
26 - Open Problems (pdf 1.11 MB)
27 - Progress report on Long Beach (pdf 530.3 KB)