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The algebra structure of linear functionals on polynomials of a single variable (Roman 1984, pp. 2-3).

A unilateral shift is a weighted shift T for which alpha_n=1 for all n.

Let A be a C^*-algebra, then two element a,b of A are called unitarily equivalent if there exists a unitary u in A such that b=uau^*.

A function f is said to have a upper bound C if f(x)<=C for all x in its domain. The least upper bound is called the supremum. A set is said to be bounded from above if it ...

The unit upper half-disk is the portion of the complex plane satisfying {|z|<=1,I[z]>0}.

The number of poles of an automorphic function in the closure of its fundamental region.

A function A such that B=del xA. The most common use of a vector potential is the representation of a magnetic field. If a vector field has zero divergence, it may be ...

The Banach space L^1([0,1]) with the product (fg)(x)=int_0^xf(x-y)g(y)dy is a non-unital commutative Banach algebra. This algebra is called the Volterra algebra.

A closed subspace of a Banach space X is called weakly complemented if the dual i^* of the natural embedding i:M↪X has a right inverse as a bounded operator. For example, the ...

Let H=l^2, (alpha_n) be a bounded sequence of complex numbers, and (xi_n) be the (usual) standard orthonormal basis of H, that is, (xi_n)(m)=delta_(nm), n,m in N, where ...