A locally compact topological group G is called an (H) group if G has a maximal compact normal subgroup with Lie factor. In this note, we study the problem when a locally compact group is an (H) group. Let G be a locally compact Hausdorff topological group. Let G0 be the identity component of G. If G/G0 is compact, then we say that G is almost connected. The structure of almost connected locall...

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).

In 2009 [Schneider 1] obtained stability estimates in terms of the BanachMazur distance for several geometric inequalities for convex bodies in an ndimensional Minkowski space En. A unique feature of his approach is to express fundamental geometric quantities in terms of a single function ρ : B×B→ R defined on the set of all convex bodies B in En. In this paper we show that (the logarithm of) t...