Booleanization of frames or uniform frames, which is not functorial under the basic choice of morphisms, becomes functorial in the categories with weakly open homomorphisms or weakly open uniform homomorphisms. Then, the construction becomes a reflection. In the uniform case, moreover, it also has a left adjoint. In connection with this, certain dual equivalences concerning uniform spaces and u...

The Banach space E has the weakly compact approximation property (W.A.P.) if there is C < ∞ so that the identity map IE can be uniformly approximated on any weakly compact subset D ⊂ E by weakly compact operators V on E satisfying ‖V ‖ ≤ C. We show that the spaces N(`, `) of nuclear operators ` → ` have the W.A.P. for 1 < q ≤ p < ∞, but that the Hardy space H does not have the W.A.P.

We give a very simple and elementary proof of the existence of a weakly compact family of probability measures {Pθ : θ ∈ Θ} to represent an important sublinear expectation— G-expectation E[·]. We also give a concrete approximation of a bounded continuous function X(ω) by an increasing sequence of cylinder functions Lip(Ω) in order to prove that Cb(Ω) belongs to the E[| · |]-completion of the Li...

Booleanization of frames or uniform frames, which is not functorial under the basic choice of morphisms, becomes functorial in the categories with weakly open homomorphisms or weakly open uniform homomorphisms. Then, the construction becomes a reflection. In the uniform case, moreover, it also has a left adjoint. In connection with this, certain dual equivalences concerning uniform spaces and u...

We present a QCD sum rule calculation for the decay constants fπ, fK using the correlation function of the axial vector mesons. Our calculations are only weakly dependent on the SU(3) breaking parameter for the QCD vacuum and gives for the ratio fK/fπ = 1.11 ± 0.02. PACS numbers: 11.30.Rd, 11.55.Hx, 14.40.-n Typeset using REVTEX E-mail: [email protected] E-mail: [email protected] 1