Computer Science/Discrete Mathematics Seminar I

In this talk I will prove the following counterpoint to a result by Kashin and Szarek (cf. Theorem 1, C. R. Acad. Sci. Paris, Ser. I, 1336 (2003) 931-936)): There exists a map \phi from infinite-dimensional euclidean space into the space of continuous complex-valued functions on [0,1], and a constant K > 0, such that for all real-valued vectors x and y, (1) the max-norm of \phi(x) is at most K times the euclidean-norm of x, (2) the inner product of x and y equals the integral over [0,1] of (\phi(x))(\phi(y)). Modulo the usual constraints, the talk will be elementary and self-contained.