On locally compact fields

Locally Compact Fields

Theorem 1. Let L be a locally compact, nondiscrete topological field. a) Then L is a finite extension of one of the following fields: (i) K = R. (ii) K = Qp. (iii) K = Fp((t)). b) In case (i) L = R or L = C. c) In case (ii) the ramification index e(L/Qp) and residual degree f(L/Qp) are uniquely determined by the abstract field L, and for any given e, f ∈ Z, the number of finite extensions L/Qp ...

Arveson Spectrum On Locally Compact Hypergroups

In this paper we study the concept of Arveson spectrum on locally compact hypergroups and for an important class of compact countable hypergroups . In thiis paper we study the concept of Arveson spectrum on locally compact hypergroups and develop its basic properties for an important class of compact countable hypergroups .

On component extensions locally compact abelian groups

Let $pounds$ be the category of locally compact abelian groups and $A,Cin pounds$. In this paper, we define component extensions of $A$ by $C$ and show that the set of all component extensions of $A$ by $C$ forms a subgroup of $Ext(C,A)$ whenever $A$ is a connected group. We establish conditions under which the component extensions split and determine LCA groups which are component projective. ...

Bracket Products on Locally Compact Abelian Groups

We define a new function-valued inner product on L2(G), called ?-bracket product, where G is a locally compact abelian group and ? is a topological isomorphism on G. We investigate the notion of ?-orthogonality, Bessel's Inequality and ?-orthonormal bases with respect to this inner product on L2(G).

P-Amenable Locally Compact Hypergroups