In mathematics, an element of a *-algebra is called unitary if it is invertible and its inverse element is the same as its adjoint element.

Definition

be a *-algebra with unit is called unitary if is unitary.

The set or

is a complete normed *-algebra) and is called a C*-algebra.

Criteria

• be a unital a normal is unitary if the spectrum consists only of elements of the circle group, i.e.

Examples

• is unitary.

be a unital C*-algebra, then:

• Every projection, as follows from the

• , then for every continuous function, if

Properties

be a unital *-algebra and Then:

• is unitary, since forms a

• is normal.

• holds for the involution

• has norm 1, i.e.

See also

• Unitary matrix

• Unitary operator

Notes

References

• English translation of