Ultraproducts of $L_1$-predual spaces

Nonstandard Analysis and Ultraproducts in Banach Spaces and Functional Analysis Lecture 1: Nonstandard Analysis and Ultraproducts of Structures

Predual Spaces of Banach Completions of Orlicz-Hardy Spaces Associated with Operators

Let L be a linear operator in L(R) and generate an analytic semigroup {e}t≥0 with kernels satisfying an upper bound of Poisson type, whose decay is measured by θ(L) ∈ (0,∞]. Let ω on (0,∞) be of upper type 1 and of critical lower type p̃0(ω) ∈ (n/(n + θ(L)), 1] and ρ(t) = t/ω(t) for t ∈ (0,∞). In this paper, the authors first introduce the VMO-type space VMOρ,L(R ) and the tent space T ω,v(R n+1...

some properties of fuzzy hilbert spaces and norm of operators

in this thesis, at first we investigate the bounded inverse theorem on fuzzy normed linear spaces and study the set of all compact operators on these spaces. then we introduce the notions of fuzzy boundedness and investigate a new norm operators and the relationship between continuity and boundedness. and, we show that the space of all fuzzy bounded operators is complete. finally, we define...

$L_1/\ell_1$-to-$L_1/\ell_1$ analysis of linear positive impulsive systems with application to the $L_1/\ell_1$-to-$L_1/\ell_1$ interval observation of linear impulsive and switched systems

Sufficient conditions characterizing the asymptotic stability and the hybrid L1/`1-gain of linear positive impulsive systems under minimum and range dwell-time constraints are obtained. These conditions are stated as infinite-dimensional linear programming problems that can be solved using sum of squares programming, a relaxation that is known to be asymptotically exact in the present case. The...

Ultraproducts of Group Rings

Group Rings Let G = g1, g2, . . . , gn be a finite group, and let k be a field. We define the group ring k[G] to be the set of sums of the form a1g1 + a2g2 + · · ·+ angn with each ai ∈ k and gi ∈ G. Addition is defined componentwise, i.e. (a1g1 + a2g2 + · · ·+ angn) + (b1g1 + b2g2 + · · ·+ bngn) = ((a1 + b1)g1 + (a2 + b2)g2 + · · ·+ (an + bn)gn). We define multiplication in the following way: (...