Related papers: An intermediate value theorem in ordered Banach sp…
We prove the existence of the invariant subspaces of some operators in a real Banach space. For example, linear isometries have invariant subspaces
Kuhn-Tucker conditions for mathematical programming problems in Banach spaces partially ordered by cone with empty interior are obtained under strong simultaneity condition. If partial ordered cone has interior point, it is proved that…
In this work we will consider integral equations defined on the whole real line and look for solutions which satisfy some certain kind of asymptotic behavior. To do that, we will define a suitable Banach space which, to the best of our…
We present here the General formulation of the problem of existence and construction of upper and lower envelope for an arbitrary function with values from the completion of the ordered set ${\rm S}$ for a certain class of functions with…
Let B be a p-uniformly convex Banach space, with p >= 2. Let T be a linear operator on B, and let A_n x denote the ergodic average (1 / n) sum_{i< n} T^n x. We prove the following variational inequality in the case where T is power bounded…
Constructing or learning a function from a finite number of sampled data points (measurements) is a fundamental problem in science and engineering. This is often formulated as a minimum norm interpolation problem, regularized learning…
We prove that every separable infinite-dimensional Banach space admits a G\^ateaux smooth and rotund norm which is not midpoint locally uniformly rotund. Moreover, by using a similar technique, we provide in every infinite-dimensional…
We consider the "order" analogues of some classical notions of Banach space geometry: extreme points and convex hulls. A Hahn-Banach type separation result is obtained, which allows us to establish an "order" Krein-Milman Theorem. We show…
We derive two fixed point theorems for a class of metric spaces that includes all Banach spaces and all complete Busemann spaces. We obtain our results by the use of a 1-Lipschitz barycenter construction and an existence result for…
We present a simple proof of the maximal monotonicity of the subdifferential operator in general Banach spaces. Using the Fitzpatrick function the Rockafellar surjectivity theorem follows as a corollary.
The main goal of this article is to show that for every (reflexive) infinite-dimensional Banach space $X$ there exists a reflexive Banach space $Y$ and $T, R \in \mathcal{L}(X,Y)$ such that $R$ is a rank-one operator, $\|T+R\|>\|T\|$ but…
We consider real spaces only. Definition. An operator $T:X\to Y$ between Banach spaces $X$ and $Y$ is called a Hahn-Banach operator if for every isometric embedding of the space $X$ into a Banach space $Z$ there exists a norm-preserving…
This paper addresses the study of novel constructions of variational analysis and generalized differentiation that are appropriate for characterizing robust stability properties of constrained set-valued mappings/multifunctions between…
While exploring dynamical systems, we often come across the principle of contraction mapping, or better known as the Banach fixed point theorem. It is an essential concept based on successive approximation, whose utility comes from two main…
In this paper, we continue the investigation of topological properties of unbounded norm (un-)topology in normed lattices. We characterize separability and second countability of un-topology in terms of properties of the underlying normed…
Similar to the theory of finite Markov chains it is shown that in a Banach space $X$ ordered by a closed cone $K$ with nonempty interior int($K$) a power bounded positive operator $A$ with compact power such that its trajectories for…
We consider linear control systems of the form $\dot{y}(t)=Ay(t)-\mu B C y(t)$ where $\mu$ is a positive real parameter, $A$ is the state operator and generates a linear $C_0-$semigroup of contractions $S(t) $ on a Banach space $X$, $B$ and…
We consider the shift operator $M_z$, defined on the Bloch space and the little Bloch space and we study the corresponding lattice of invariant subspaces. The index of a closed invariant subspace $E$ is defined as $\text{ind}(E) =…
A final-state observability result in the Banach space setting for non-autonomous observation problems is obtained that covers and extends all previously known results in this context, while providing a streamlined proof that follows the…
In this paper, the convergence of alternating minimization is established for non-smooth convex optimization in Banach spaces, and novel rates of convergence are provided. As objective function a composition of a smooth and a non-smooth…