Inmathematics, an element of a *-algebra is called unitary if it is invertible and its inverse element is the same as its adjoint element.[1]
Let be a *-algebra with unit
. An element
is called unitary if
. In other words, if
is invertible and
holds, then
is unitary.[1]
The set of unitary elements is denoted by or
.
A special case from particular importance is the case where is a complete normed *-algebra. This algebra satisfies the C*-identity (
) and is called a C*-algebra.
Let be a unital C*-algebra, then:
Let be a unital *-algebra and
. Then:
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Basic concepts |
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Main results |
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Special Elements/Operators |
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Spectrum |
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Decomposition |
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Spectral Theorem |
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Special algebras |
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Finite-Dimensional |
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Generalizations |
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Miscellaneous |
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Examples |
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Applications |
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