w,q = supφ∈BX́ ( ∑k j=1 | φ(xj) | ) 1 q . This is a natural generalization of the concept of (p; q)-summing operators and in the last years has been studied by several authors. The infimum of the L > 0 for which the inequality holds defines a norm ‖.‖as(p;q) for the case p ≥ 1 or a p-norm for the case p < 1 on the space of (p; q)-summing homogeneous polynomials. The space of all m-homogeneous (p...

Let L be a linear space of real bounded random variables on the probability space (Ω,A, P0). There is a finitely additive probability P on A, such that P ∼ P0 and EP (X) = 0 for all X ∈ L, if and only if c EQ(X) ≤ ess sup(−X), X ∈ L, for some constant c > 0 and (countably additive) probability Q on A such that Q ∼ P0. A necessary condition for such a P to exist is L− L∞ ∩ L∞ = {0}, where the cl...

Let L be a linear space of real bounded random variables on the probability space (Ω,A, P0). There is a finitely additive probability P on A, such that P ∼ P0 and EP (X) = 0 for all X ∈ L, if and only if c EQ(X) ≤ ess sup(−X), X ∈ L, for some constant c > 0 and (countably additive) probability Q on A such that Q ∼ P0. A necessary condition for such a P to exist is L − L+∞ ∩ L + ∞ = {0}, where t...

The overlap formalism of chiral fermions provides a tool to measure the index, Q, of the chiral Dirac operator in a fixed gauge field background on the lattice. This enables a numerical measurement of the probability distribution, p(Q), in Yang-Mills theories. We have obtained an estimate for p(Q) in pure SU(2) gauge theory by measuring Q on 140 independent gauge field configurations generated ...

We report improved frequency ratio measurement with $^{87}$Sr and $^{171}$Yb optical lattice clocks at the National Metrology Institute of Japan (NMIJ). The clock is enhanced several major modifications re-evaluated a reduced uncertainty $1.1\times10^{-16}$. employed an $4\times10^{-16}$ that was developed for contributing to International Atomic Time (TAI). result $\nu_{\mathrm{Yb}}/\nu_{\math...

We prove that every strictly positive endofunctor on the category of sets generated by Martin-LL of's extensional type theory has an initial algebra. This representation of inductively deened sets uses essentially the wellorderings introduced by Martin-LL of in \Constructive Mathematics and Computer Programming". 1 Background Martin-LL of 10] introduced a general set former for wellorderings in...

We complete the quasi-isometric classification of irreducible lattices in semisimple Lie groups over nondiscrete locally compact fields of characteristic zero by showing that any quasi-isometry of a rank one S-arithmetic lattice in a semisimple Lie group over nondiscrete locally compact fields of characteristic zero is a finite distance in the sup-norm from a commensurator.

We introduce the concept of a Girard couple, which consists of two (not necessarily unital) quantales linked by a strong form of duality. The two basic examples of Girard couples arise in the study of endomorphism quantales and of the spectra of operator algebras. We construct, for an arbitrary sup-lattice S, a Girard quantale whose right-sided part is isomorphic to S.

We prove that if q is in (1,∞), Y is a Banach space, and T is a linear operator defined on the space of finite linear combinations of (1, q)-atoms in R with the property that sup{‖Ta‖Y : a is a (1, q)-atom} < ∞, then T admits a (unique) continuous extension to a bounded linear operator from H(R) to Y . We show that the same is true if we replace (1, q)-atoms by continuous (1,∞)-atoms. This is k...