Unitary Element
Let A be a unital C^*-algebra. An element u in A is called unitary if u^*u=uu^*=1.
For example, for each self-adjoint element a in A, the element
is unitary, but the converse is not true in general (Kadison and Ringrose 1997).
This entry contributed by Mohammad Sal Moslehian
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References
Kadison, R. V. and Ringrose, J. R. Fundamentals of the Theory of Operator Algebras, Vol. 1: Elementary Theory. Providence, RI: Amer. Math. Soc., 1997.Murphy, G. J. C-*-Algebras and Operator Theory. New York: Academic Press, 1990.Referenced on Wolfram|Alpha
Unitary ElementCite this as:
Moslehian, Mohammad Sal. "Unitary Element." From MathWorld--A Wolfram Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/UnitaryElement.html