# Mathematician:Claude Ambrose Rogers

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## 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**.