An infinite-dimensional version of Liapunov's convexity theorem.

An Infinite Dimensional Version of a Theorem of Bernstein

1. Introduction. Let (R") is the algebra Q1(Rn) of all real-valued functions of class C1. In other words, for every fEG1(Rn) there is a sequence {pn} of polynomials such that pn—*/ uniformly o...

An Infinite Dimensional Convolution Theorem

An Infinite Dimensional Convolution Theorem

An Infinite Dimensional Convolution Theorem

Determinant Preserving Maps: an Infinite Dimensional Version of a Theorem of Frobenius

In this paper we investigate the structure of maps on classes of Hilbert space operators leaving the determinant of linear combinations invariant. Our main result is an infinite dimensional version of the famous theorem of Frobenius about determinant preserving linear maps on matrix algebras. In that theorem of ours, we use the notion of (Fredholm) determinant of bounded Hilbert space operators...