ﻻ يوجد ملخص باللغة العربية
Unbounded order convergence has lately been systematically studied as a generalization of almost everywhere convergence to the abstract setting of vector and Banach lattices. This paper presents a duality theory for unbounded order convergence. We define the unbounded order dual (or uo-dual) $X_{uo}^sim$ of a Banach lattice $X$ and identify it as the order continuous part of the order continuous dual $X_n^sim$. The result allows us to characterize the Banach lattices that have order continuous preduals and to show that an order continuous predual is unique when it exists. Applications to the Fenchel-Moreau duality theory of convex functionals are given. The applications are of interest in the theory of risk measures in Mathematical Finance.
The main result (roughly) is that if (H_i) converges weakly to H and if also f(H_i) converges weakly to f(H), for a single strictly convex continuous function f, then (H_i) must converge strongly to H. One application is that if f(pr(H)) = pr(f(H)),
In 2012 Gu{a}vruc{t}a introduced the notions of $K$-frame and of atomic system for a linear bounded operator $K$ in a Hilbert space $mathcal{H}$, in order to decompose its range $mathcal{R}(K)$ with a frame-like expansion. In this article we revisit
Let $d$ be a positive integer, and let $mu$ be a finite measure on $br^d$. In this paper we ask when it is possible to find a subset $Lambda$ in $br^d$ such that the corresponding complex exponential functions $e_lambda$ indexed by $Lambda$ are ortho
We present a constructive proof of Gelfand duality for C*-algebras by reducing the problem to Gelfand duality for real C*-algebras.
In this paper we {em discuss} diverse aspects of mutual relationship between adjoints and formal adjoints of unbounded operators bearing a matrix structure. We emphasize on the behaviour of row and column operators as they turn out to be the germs of