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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

 u=exp(ia)=sum_(n=0)^infty((ia)^n)/(n!)

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.

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Unitary Element

Cite this as:

Moslehian, Mohammad Sal. "Unitary Element." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/UnitaryElement.html

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