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A W^*-algebra is a C-*-algebra A for which there is a Banach space A_* such that its dual is A. Then the space A_* is uniquely defined and is called the pre-dual of A. Every ...

The commutator series of a Lie algebra g, sometimes called the derived series, is the sequence of subalgebras recursively defined by g^(k+1)=[g^k,g^k], (1) with g^0=g. The ...

Let A be a non-unital C^*-algebra. There is a unique (up to isomorphism) unital C^*-algebra which contains A as an essential ideal and is maximal in the sense that any other ...

A Jordan algebra which is not isomorphic to a subalgebra.

A Jordan algebra which is isomorphic to a subalgebra.

There are no fewer than three distinct notions of the term local C^*-algebra used throughout functional analysis. A normed algebra A=(A,|·|_A) is said to be a local ...

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.

Let A be any algebra over a field F, and define a derivation of A as a linear operator D on A satisfying (xy)D=(xD)y+x(yD) for all x,y in A. Then the set D(A) of all ...

Let P be a class of (universal) algebras. Then an algebra A is a local P-algebra provided that every finitely generated subalgebra F of A is a member of the class P. Note ...

Computer algebra is a diffuse branch of mathematics done with computers that encompasses both computational algebra and analysis.