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

A uniquely complemented lattice is a complemented lattice (L, ^ , v ,0,1,^') that satisfies ( forall x in L)( forall y in L)[(x ^ y=0) ^ (x v y=1)]=>y=x^'. The class of ...

An R-module M is said to be unital if R is a commutative ring with multiplicative identity 1=1_R and if 1m=m for all elements m in M.

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 universal sentence is a sentence (i.e., formula of the predicate calculus without free variables) whose variables are universally quantified.

An unknown is an independent variable of a function. A function with n independent variables is said to be a function "in," "with," or "of" n unknowns.

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 ...

For every topological T1-space X, the following conditions are equivalent. 1. X is regular and second countable, 2. X is separable and metrizable. 3. X is homeomorphic to a ...

Let (K,|·|) be a valuated field. The valuation group G is defined to be the set G={|x|:x in K,x!=0}, with the group operation being multiplication. It is a subgroup of the ...

Let (K,|·|) be a non-Archimedean field. Its valuation ring R is defined to be R={x in K:|x|<=1}. The valuation ring has maximal ideal M={x in K:|x|<1}, and the field R/M is ...