Mathematician:Claude Ambrose Rogers

Mathematician

English mathematician who worked in analysis and geometry.

Nationality

English

History

• Born: 1 November 1920 in Cambridge, Cambridgeshire, England
• Died: 5 December 2005 in Islington, London, England

Theorems and Definitions

• Dvoretzky-Rogers Lemma (with Aryeh Dvoretzky)
• Dvoretzky-Rogers Theorem (with Aryeh Dvoretzky)
• Rogers Bound

Publications

• 1946: Linear Transformations Which Apply To All Convergent Sequences and Series (J. London Math. Soc. Vol. 21: pp. 123 – 128)

• 1946: A note on a theorem of Blichfeldt

• 1947: Hlawka's theorem in the geometry of numbers (with Harold Davenport)

• 1947: A note on a problem of Mahler

• 1947: A note on irreducible star bodies

• 1947: Existence Theorems in the Geometry of Numbers (Ann. Math. Ser. 2 Vol. 48: pp. 994 – 1002)  www.jstor.org/stable/1969390

• 1948: The critical determinant of a convex cylinder (with J.H.H. Chalk)

• 1948: A problem of Hirsch

• 1949: The product of the minima and the determinant of a set

• 1949: The product of $n$ homogeneous linear forms

• 1949: The successive minima of measurable sets

• 1949: On the critical determinant of a certain nonconvex cylinder

• 1949: A note on the geometry of numbers (with Harold Davenport)

• 1949: The successive minima of a convex cylinder (with J.H.H. Chalk)

• 1950: The Asymptotic Directions of $n$ Linear Forms in $n+1$ Integral Variables (Proc. London Math. Soc. Ser. 2 Vol. 52: pp. 161 – 185)

• 1950: The Signatures of the Errors of Simultaneous Diophantine Approximations (Proc. London Math. Soc. Ser. 2 Vol. 52: pp. 186 – 190)

• 1950: The Transformation of Sequences by Matrices (Proc. London Math. Soc. Ser. 2 Vol. 52: pp. 321 – 364)

• 1950: A note on coverings and packings

• 1950: Absolute and unconditional convergence in normed linear spaces (with Aryeh Dvoretzky)

• 1953: The covering of $n$-dimensional space by spheres (with Paul Erdős)

• 1958: The packing of equal spheres (Proc. London Math. Soc. Ser. 3 Vol. 8: pp. 609 – 620)

• 1961: Covering space with convex bodies (with Paul Erdős)

• 1964: Packing and Covering

• 1964: The Brunn-Minkowski theorem and related inequalities (lecture at the British Mathematical Colloquium)

• 1970: Hausdorff Measures

• 2002: Selectors (with John E. Jayne)

Notable Quotes

Many mathematicians believe, and all physicists know, that the density cannot exceed $\dfrac \pi {\sqrt {18} }$.

Also known as

Known throughout his life as Ambrose.

Sources

• John J. O'Connor and Edmund F. Robertson: "Claude Ambrose Rogers": MacTutor History of Mathematics archive