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A closed ideal I in a C^*-algebra A is called essential if I has nonzero intersection with every other nonzero closed ideal A or, equivalently, if aI={0} implies a=0 for all ...

A bounded operator U on a Hilbert space H is called essentially unitary if U^*U-I and UU^*-I are compact operators.

An extreme point of a subset K of a vector space X is an extreme set S of K which consists of a single point x in K. The collection of all extreme points of K is sometimes ...

The flat norm on a current is defined by F(S)=int{Area T+Vol(R):S-T=partialR}, where partialR is the boundary of R.

The Gelfand-Naimark theorem states that each C^*-algebra is isometrically *-isomorphic to a closed *-subalgebra of the algebra B(H) consisting of all bounded operators acting ...

If A is a unital Banach algebra where every nonzero element is invertible, then A is the algebra of complex numbers.

Let A be a C^*-algebra. A C^*-subalgebra (that is a closed *-subalgebra) B of A is called hereditary if bab^' in B for all b,b^' in B and a in A, or equivalently if for a in ...

A Hilbert basis for the vector space of square summable sequences (a_n)=a_1, a_2, ... is given by the standard basis e_i, where e_i=delta_(in), with delta_(in) the Kronecker ...

An inner product space is a vector space together with an inner product on it. If the inner product defines a complete metric, then the inner product space is called a ...

An involutive Banach algebra is a Banach algebra A which is an involutive algebra and ||a^*||=||a|| for all a in A.