Topological inner invariant means

Abstract

For a locally compact group G, we investigate topological inner invariant means on L8(G) and its subspaces. In particular, we characterize strict inner amenability of L1(G) to study the relation between this notion and strict inner amenability of G.

Extention of topological inner invariant means

“…Now we give a simpler proof based on the technic used in [7,Th.3.2] for the following well known theorem , see [9].…”

“…In [7] authors study locally compact groups for which L ∞ (G) has a TIIM whose restriction to C b (G) is not δ e . In this paper we show that a TIIM on LUC(G) (space of left uniformly continuous functions on G) has a topological inner invariant extension to L ∞ (G).…”

“…In this paper we show that a TIIM on LUC(G) (space of left uniformly continuous functions on G) has a topological inner invariant extension to L ∞ (G). Also based on the technic used in [7,Th.3.2] we give a simpler proof of the well known fact that amenability implies topological amenability (see [9]). …”

A generalization of amenability and inner amenability of groups

“…The study of inner invariant means was initiated by Effros [6] and pursued by Lau and Paterson [14]. Recently, several authors have studied means on L ∞ (G) that are invariant under the inner automorphisms of G (see [10], [1], [15], [17], [23] and [24]). …”

Inner invariant means on a locally compact group

“…We shall follow Hewitt [3] and Yuan [10] for definitions and terminologies not explained here. The literature on inner amenability has grown substantially in recent years (see [5], [6], [7] and [12]). …”