In mathematics, especially functional analysis, a Banach algebra, named after Stefan Banach, is an associative algebra A over the real or complex numbers which at the same time is also a Banach space.

In mathematics, especially functional analysis, a normal operator on a complex Hilbert space is a continuous linear operator

In mathematics, especially functional analysis, a self-adjoint ( or hermitian ) element of a C *- algebra is called positive if its spectrum consists of non-negative real numbers.

In mathematics, especially functional analysis, the spectrum of an operator generalizes the notion of eigenvalues.

In mathematics, especially functional analysis, Bessel's inequality is a statement about the coefficients of an element in a Hilbert space with respect to an orthonormal sequence.

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