We characterize compact composition operators on real Banach spaces of complex-valued bounded Lipschitz functions on metric spaces, not necessarily compact, with Lipschitz involutions and determine their spectra.

The notion of simple compact quantum group is introduced. As non-trivial (noncommutative and noncocommutative) examples, the following families of compact quantum groups are shown to be simple: (a) The universal quantum groups Bu(Q) for Q ∈ GL(n,C) satisfying QQ̄ = ±In, n ≥ 2; (b) The quantum automorphism groups Aaut(B, τ) of finite dimensional C ∗-algebras B endowed with the canonical trace τ w...

It is our purpose to study curvature structures of compact hypersurfaces in the unit sphere S(1). We proved that the Riemannian product S( √ 1 − c2) ×Sn−1(c) is the only compact hypersurfaces in S(1) with infinite fundamental group, which satisfy r ≥ n−2 n−1 and S ≤ (n − 1)n(r−1)+2 n−2 + n−2 n(r−1)+2 , where n(n − 1)r is the scalar curvature of hypersurfaces and c = n−2 nr . In particular, we o...

We describe a C compiler tailored to save space in executables. It accepts an arbitrary C program and customizes for it a compact interpreter and interpretive code. In a typical application, the compiler halves its own size. We have written programs that collaborate to compile an arbitrary C program into a compact interpreter and interpretive code. It improves on prior efforts to automatically ...

We give a hyperkk ahler analogue of the classiication of compact homogeneous KK ahler manifolds. Namely we show that, for a compact semisimple Lie group G, the complete G-invariant hyperkk ahler manifolds which are also locally G c-homogeneous with respect to one of the complex structures are precisely the hy-perkk ahler metrics of Kronheimer, Biquard and Kovalev on coadjoint semisimple orbits ...

Let  $varpi$ be a representation of the homogeneous space $G/H$, where $G$ be a locally compact group and  $H$ be a compact subgroup of $G$. For  an admissible wavelet $zeta$ for $varpi$  and $psi in L^p(G/H), 1leq p <infty$, we determine a class of bounded  compact operators  which are related to continuous wavelet transforms on homogeneous spaces and they are called localization operators.

In this chapter, we begin to discuss the ways in which R differs from C[0,1]. In particular, we compare the characterization of compact subsets of R by HeineBorel with the characterization of compact subsets of C[0,1] by Arzela-Ascoli. We find that subsets of C[0,1] must satisfy more conditions than subsets of R if they are to be compact. Before we can begin to investigate this, we have a few p...

In this paper we give some necessary and sufficient conditions for which each Banach lattice  is    space and we study some properties of b-weakly compact operators from a Banach lattice  into a Banach space . We show that every weakly compact operator from a Banach lattice  into a Banach space  is b-weakly compact and give a counterexample which shows that the inverse is not true but we prove ...