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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.〔
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The theorem was published by B. Russo and H. A. Dye in 1966.〔
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==Other formulations and generalizations==
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.〔
A more precise result is true for the C
*-algebra of all bounded linear operators on a Hilbert space: If ''T'' is such an operator and ||''T''|| < 1 − 2/''n'' for some integer ''n'' > 2, then ''T'' is the mean of ''n'' unitary operators.〔
〕
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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