In this paper, we investigate local properties in the system of completely 1-summing mapping spaces. We introduce notions injectivity, reflexivity, exactness, nuclearity and finite-representability First obtain that if V has WEP, is locally reflexive (Ⅱ1(⋅,⋅), π1(⋅)) only it (Ⅰ(⋅,⋅), t(⋅)). Furthermore prove an operator space ⊆ B(H) exact finitely representable {Mn}n∈N π1(⋅)). At last, show = C.

We discuss the φ and φ theory defined in a flat D-dimensional space-time. We assume that the system is in equilibrium with a thermal bath at temperature β−1. To obtain non-perturbative result, the 1/N expansion is used. The method of the composite operator (CJT) for summing a large set of Feynman graphs, is developed for the finite temperature system. The ressumed effective potential and the an...

Abstract This paper explores the possibility for summing Fourier series nonlinearly via Pythagorean harmonic mean. It reports on new results this summability with introduction of concepts like smoothing operator and semi-harmonic summation. The is demonstrated to be Kalman filtering linear summability, logistic processing linearized summability. An emerging direct inapplicability seismic-like s...

In this note we study some basic properties of the γinterpolation method introduced in [6] e.g. interpolation of Bochner spaces and interpolation of analytic operator valued functions in the sense of Stein. As applications we consider the interpolation of almost summing operators (in particular γ-radonifying and Hilbert-Schmidt operators) and of γ-Sobolev spaces as introduced in [6]. We also co...

We study the question of whether or not contractive representations of logmodular algebras are completely contractive. We prove that a 2-contractive representation of a logmodular algebra extends to a positive map on the enveloping C∗-algebra, which we show generalizes a result of Foias and Suciu on uniform logmodular algebras. Our proof uses non-commutative operator space generalizations of cl...

This work focuses on Conrady-Hnybida's four-dimensional extended spinfoam model with timelike polyhedra, while we restrict all faces to be spacelike. First, prove the absolute convergence of vertex amplitude when $\mathrm{SU}(1,1)$ boundary states are coherent or canonical basis, their finite linear combinations. Second, based and a proper prescription intertwiner space, construct an arbitrary ...

Let T (t), 0 ≤ t < ∞, be a one parameter c0-semigroup of bounded linear operators on a Banach space X with infinitesimal generator A and R(λ, A) be the resolvent operator of A. The Hille-Yosida Theorem for c0-semigroups asserts that the resolvent operator of the infinitesimal generator A satisfies ‖R(λ, A)‖ ≤ M λ−ω for some constants M > 0 and λ ∈ R (the set of real numbers), λ > ω. The object ...