Claude Ambrose Rogers

Claude Ambrose Rogers FRS(1 November 1920 – 5 December 2005) was an English mathematician who worked in analysis and geometry.

Much of his work concerns the theory of normed spaces and convex geometry. In the theory of Banach spaces and summability, he proved the Dvoretzky–Rogers lemma and the Dvoretzky–Rogers theorem, both with Aryeh Dvoretzky.^[1][2][3][4] He constructed a counterexample to a conjecture related to the Busemann–Petty problem. In the geometry of numbers, the Rogers bound is a bound for dense packings of spheres.

Rogers was elected a fellow of the Royal Society in 1959.

Publications

• Rogers, C. A. (1964), Packing and covering, Cambridge Tracts in Mathematics and Mathematical Physics, No. 54, Cambridge University Press, ISBN 978-0-521-06121-6, MR0172183, http://books.google.com/books?id=kS2pPwAACAAJ 
• Rogers, C. A. (1970), Hausdorff measures, Cambridge University Press, ISBN 978-0-521-62491-6, MR0281862, http://books.google.com/books?id=XFZFz_04tw4C 
• Rogers, C. Ambrose (1975), "Probabilistic and combinatorial methods in the study of the geometry of Euclidean spaces", Proceedings of the International Congress of Mathematicians (Vancouver, B. C., 1974), Vol. 1, Canad. Math. Congress, Montreal, Que., pp. 497–500, MR0423192, http://mathunion.org/ICM/ICM1974.1/ 
• Jayne, John E.; Rogers, C. Ambrose (2002), Selectors, Princeton University Press, ISBN 978-0-691-09628-5, MR1915965, http://press.princeton.edu/titles/7322.html 

References

1. ^ Diestel, J. (1984). Sequences and series in Banach spaces. Graduate Texts in Mathematics. 92. Springer-Verlag. ISBN 0-387-90859-5. MR737004. 
2. ^ Diestel, Joseph; Jarchow, Hans; Tonge, Andrew (1995). Absolutely summing operators. Cambridge University Press. pp. 90–91. ISBN 0521431689. 
3. ^ Kadets, V. M.; Kadets, M. I. (1991). Rearrangements of series in Banach spaces. Translations of Mathematical Monographs. 86 (Translated by Harold H. McFaden from the Russian-language (Tartu) 1988 ed.). Providence, RI: American Mathematical Society. pp. iv+123. ISBN 0-8218-4546-2. MR1108619. 
4. ^ Kadets, Mikhail I.; Kadets, Vladimir M. (1997). Series in Banach spaces: Conditional and unconditional convergence. Operator Theory: Advances and Applications. 94 (Translated by Andrei Iacob from the Russian-language ed.). Basel: Birkhäuser Verlag. pp. viii+156. ISBN 3-7643-5401-1. MR1442255. 

External resources

• Larman, David, "Ambrose Rogers", L. M. S. Newsletter, Obituary, http://old.lms.ac.uk/newsletter/344/344_08.html 
• O'Connor, John J.; Robertson, Edmund F., "Claude Ambrose Rogers", MacTutor History of Mathematics archive, University of St Andrews, http://www-history.mcs.st-andrews.ac.uk/Biographies/Rogers.html .
• Claude Ambrose Rogers at the Mathematics Genealogy Project.