A unitary element 
of a unital C*-algebra 
satisfies 
.
For example, for each self-adjoint element 
, the element
 |
is unitary, but the converse is not true in general (Kadison and Ringrose 1997).
Unitary Element
See also
C*-Algebra Isometry, Cocycle Conjugacy, Irrational Rotation Algebra, Jiang-Su StabilityThis 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:
Weisstein, Eric W., with contributions by Mohammad Sal Moslehian. "Unitary Element." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/UnitaryElement.html