Unitary element

In mathematics, an element x of a *-algebra is unitary if $x^{*}=x^{-1}$.

In functional analysis, a linear operator A from a Hilbert space into itself is called unitary if it is invertible and its inverse is equal to its own adjoint A^∗ and that the domain of A is the same as that of A^∗. See unitary operator for a detailed discussion. If the Hilbert space is finite-dimensional and an orthonormal basis has been chosen, then the operator A is unitary if and only if the matrix describing A with respect to this basis is a unitary matrix.

See also

• Normal element
• Self-adjoint
• Unitary matrix

References

• Reed, M.; Simon, B. (1972). Methods of Mathematical Physics. Vol 2. Academic Press.
• Teschl, G. (2009). Mathematical Methods in Quantum Mechanics; With Applications to Schrödinger Operators. Providence: American Mathematical Society.
• Schaefer, Helmut H. (1999). Topological Vector Spaces. GTM. Vol. 3. New York, NY: Springer New York Imprint Springer. ISBN 978-1-4612-7155-0. OCLC 840278135. {{cite book}}: Invalid |ref=harv (help)