Let G be a locally compact, totally disconnected, Hausdorff topological group with a neighborhood basis {Ki}i of the identity consisting of compact, open, normal subgroups. Often K ⊂ G will denote a compact, open subgroup of G. We consider representations (ρ, V ) of G, where V is often infinite-dimensional. We say the representation is smooth if V = ∪KV K , i.e., if every v ∈ V is fixed by some...

In this note we characterize the compact weighted Frobenius-Perron operator $p$ on $L^1(Sigma)$ and determine their spectra. We also show that every weakly compact weighted Frobenius-Perron operator on $L^1(Sigma)$ is compact.

Let $L$ be a completely regular frame and $mathcal{R}L$ be the ring of real-valued continuous functions on $L$. We consider the set $$mathcal{R}_{infty}L = {varphi in mathcal{R} L : uparrow varphi( dfrac{-1}{n}, dfrac{1}{n}) mbox{ is a compact frame for any $n in mathbb{N}$}}.$$ Suppose that $C_{infty} (X)$ is the family of all functions $f in C(X)$ for which the set ${x in X: |f(x)|geq dfrac{1...

in this paper, a complete description concerning linear operators of banach spaces with range in lipschitz algebras $lip_al(x)$ is provided. necessary and sufficient conditions are established to ensure boundedness and (weak) compactness of these operators. finally, a lower bound for the essential norm of such operators is obtained.

the purpose of this paper is to introduce the concept of pairwise f-closedness in bitopological spaces. this space contains both of pairwise strongcompactness and pairwise s-closedness and contained in pairwise quasi h-closedness. the characteristics and relationships concerning this new class ofspaces with other corresponding types are established. moreover, several ofits basic and important p...

Let X $X$ be a compact complex space in Fujiki's Class C $\mathcal {C}$ . We show that the group Aut ( ) $\operatorname{Aut}(X)$ of all biholomorphic automorphisms has Jordan property: there is (Jordan) constant J = $J J(X)$ such any finite subgroup G ⩽ $G\leqslant \operatorname{Aut}(X)$ an abelian H $H\leqslant G$ with index [ : ] $[G:H]\leqslant J$ This extends, quite different method, result...