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Let G be an algebraic group. G together with the discrete topology is a locally compact group and one may consider the counting measure as a left invariant Haar measure on G. ...

A disk algebra is an algebra of functions which are analytic on the open unit disk in C and continuous up to the boundary. A representative measure for a point x in the ...

Let A be a C^*-algebra and A_+ be its positive part. Suppose that E is a complex linear space which is a left A-module and lambda(ax)=(lambdaa)x=a(lambdax), where lambda in ...

A Fréchet space is a complete and metrizable space, sometimes also with the restriction that the space be locally convex. The topology of a Fréchet space is defined by a ...

If X is a locally compact T2-space, then the set C_ degrees(X) of all continuous complex valued functions on X vanishing at infinity (i.e., for each epsilon>0, the set {x in ...

The Gelfand transform x|->x^^ is defined as follows. If phi:B->C is linear and multiplicative in the senses phi(ax+by)=aphi(x)+bphi(y) and phi(xy)=phi(x)phi(y), where B is a ...

The group algebra K[G], where K is a field and G a group with the operation *, is the set of all linear combinations of finitely many elements of G with coefficients in K, ...

If 0<p<infty, then the Hardy space H^p(D) is the class of functions holomorphic on the disk D and satisfying the growth condition ...

Let H be a Hilbert space and (e_i)_(i in I) is an orthonormal basis for H. The set S(H) of all operators T for which sum_(i in I)||Te_i||^2<infty is a self-adjoint ideal of ...

Suppose that A is a Banach algebra and X is a Banach A-bimodule. For n=0, 1, 2, ..., let C^n(A,X) be the Banach space of all bounded n-linear mappings from A×...×A into X ...