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Any symmetric polynomial (respectively, symmetric rational function) can be expressed as a polynomial (respectively, rational function) in the elementary symmetric ...

There are two different statements, each separately known as the greatest common divisor theorem. 1. Given positive integers m and n, it is possible to choose integers x and ...

Given an m×n matrix A, the fundamental theorem of linear algebra is a collection of results relating various properties of the four fundamental matrix subspaces of A. In ...

A Banach algebra A for which H^1(A,X^*)=Z^1(A,X^*)/B^1(A,X^*)=0 for all Banach A-bimodules X is called amenable (or Johnson amenable; Helemskii 1989, 1997). This notion was ...

If A is a normed algebra, a net {e_i} in A is called an approximate identity for A if sup_(i)|e_i|<infty and if for each a in A, e_ia->a and ae_i->a. Though this definition ...

The approximation problem is a well known problem of functional analysis (Grothendieck 1955). It asks to determine whether every compact operator T from a Banach space X to a ...

Let A be a commutative complex Banach algebra. A nonzero homomorphism from A onto the field of complex numbers is called a character. Every character is automatically ...

Let A be the area of a simply closed lattice polygon. Let B denote the number of lattice points on the polygon edges and I the number of points in the interior of the ...

For every positive integer n, there exists a sphere which has exactly n lattice points on its surface. The sphere is given by the equation ...

If n=1,2 (mod 4), and the squarefree part of n is divisible by a prime p=3 (mod 4), then no difference set of order n exists. Equivalently, if a projective plane of order n ...