Russo–Dye theorem

In mathematics, the Russo–Dye theorem is a result in the field of functional analysis.

It states that in a unital C*-algebra, the closure of the convex hull of the unitary elements is the closed unit ball.

[2] Results similar to the Russo–Dye theorem hold in more general contexts.

For example, in a unital *-Banach algebra, the closed unit ball is contained in the closed convex hull of the unitary elements.

[3]: 98 This example is due to Russo & Dye,[2] Corollary 1: If U(A) denotes the unitary elements of a C*-algebra A, then the norm of a linear mapping f from A to a normed linear space B is In other words, the norm of an operator can be calculated using only the unitary elements of the algebra.