In earlier papers we studied direct limits (G,K) = lim −→ (Gn,Kn) of two types of Gelfand pairs. The first type was that in which the Gn/Kn are compact riemannian symmetric spaces. The second type was that in which Gn = Nn ⋊ Kn with Nn nilpotent, in other words pairs (Gn,Kn) for which Gn/Kn is a commutative nilmanifold. In each we worked out a method inspired by the Frobenius–Schur Orthogonalit...

This paper focuses on the relationships between stratified $L$-conver-gence spaces, stratified strong $L$-convergence spaces and stratifiedlevelwise  $L$-convergence spaces. It has been known that: (1) astratified $L$-convergence space is precisely a left-continuousstratified levelwise $L$-convergence space; and (2) a  stratifiedstrong $L$-convergence space is naturally a stratified $L$-converg...

We generalize Lück’s Theorem to show that the L-Betti numbers of a residually amenable covering space are the limit of the L-Betti numbers of a sequence of amenable covering spaces. We show that any residually amenable covering space of a finite simplicial complex is of determinant class, and that the L torsion is a homotopy invariant for such spaces. We give examples of residually amenable gro...

Let L be an Orlicz space defined by a convex Orlicz function φ and let E be the space of finite elements in L (= the ideal of all elements of order continuous norm). We show that the usual norm topology Tφ on L restricted to E can be obtained as an inductive limit topology with respect to some family of other Orlicz spaces. As an application we obtain a characterization of continuity of linear ...

we study different completeness definitions for two categories of lattice-valued cauchy spaces and the relations between these definitions. we also show the equivalence of a so-called completion axiom and the existence of a completion.

converge a.e. for all f in L log log(L) but fail to have a finite limit for an f ∈ L. In fact, we show that for each Orlicz space properly contained in L, 1 ≤ q < ∞, there is a sequence along which the ergodic averages converge for functions in the Orlicz space, but diverge for all f ∈ L . This extends the work of K. Reinhold, who, building on the work of A. Bellow, constructed a sequence for w...

First, we recall some notations and definitions which will be used throughout the paper (cf. [12]). A double sequence x = (xjk) of real or complex numbers is said to be bounded if ‖x‖∞ = supj,k |xjk| < ∞. We denote the space of all bounded double sequences by L. A double sequence x = (xjk) is said to converge to the limit L in Pringsheims sense (shortly, p-convergent to L) if for every ε > 0 th...