相关论文: On k-smoothness of operators between Banach spaces

We study $k-$smoothness of bounded linear operators defined between arbitrary Banach spaces. As an application, we characterize $k-$smooth operators defined from $\ell_1^n$ to an arbitrary Banach space. We also completely characterize…

We characterize $k-$smoothness of bounded linear operators defined between infinite-dimensional Hilbert spaces. We study the problem in the setting of both finite and infinite-dimensional Banach spaces. We also characterize $k-$smoothness…

We characterize $k-$smoothness of an element on the unit sphere of a finite-dimensional polyhedral Banach space. Then we study $k-$smoothness of an operator $T \in \mathbb{L}(\ell_{\infty}^n,\mathbb{Y}),$ where $\mathbb{Y}$ is a…

We study the smoothness and the norm attainment of bounded bilinear operators between Banach spaces, using the concepts of Birkhoff-James orthogonality and semi-inner-products. In the finite-dimensional case, we characterize Birkhoff-James…

We provide a comprehensive study of interrelations between different measures of smoothness of functions on various domains and smoothness properties of approximation processes. Two general approaches to this problem have been developed:…

We characrterize extreme contractions defined between \ finite-dimensional polyhedral Banach spaces using $k$- smoothness of operators. We also explore weak L-P property, a recently introduced concept in the study of extreme contractions.…

Given a nonzero positive operator $A$ on a Hilbert space $\mathbb{H}$, a semi-inner product is naturally induced on $\mathbb{H}$. In this work, we introduce the notion of \emph{$A$-smoothness} for bounded linear operators on the resulting…

We present a sufficient condition for smoothness of bounded linear operators on Banach spaces for the first time. Let $T, A \in B(\mathbb{X}, \mathbb{Y}),$ where $\mathbb{X}$ is a real Banach space and $\mathbb{Y}$ is a real normed linear…

We completely characterize smoothness of bounded linear operators between infinite dimensional real normed linear spaces, probably for the very first time, by applying the concepts of Birkhoff-James orthogonality and semi-inner-products in…

In topological equivalence, a bounded linear operator between Banach spaces - we focus on the case of Hilbert spaces - is viewed as only acting linearly and continuously between them qua different spaces with the structure of linear…

Let $X, Y$ be infinite dimensional, Banach spaces. Let $\mathcal{L}(X, Y)$ be the space of bounded operators . Motivated by the fact that smoothness of norm in the higher duals of even order of a Banach space can lead to Frechet…

We investigate the local preservation of Birkhoff-James orthogonality at a point by a linear operator on a finite-dimensional Banach space and illustrate its importance in understanding the action of the operator in terms of the geometry of…

The aim of this manuscript is to study \emph{spear operators}: bounded linear operators $G$ between Banach spaces $X$ and $Y$ satisfying that for every other bounded linear operator $T:X\longrightarrow Y$ there exists a modulus-one scalar…

We study uniform $\epsilon-$BPB approximations of bounded linear operators between Banach spaces from a geometric perspective. We show that for sufficiently small positive values of $\epsilon,$ many geometric properties like smoothness,…

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 article introduces classes of normal and unitary operators on smooth Banach spaces, providing extensions of the classical notions of normal and unitary operators from Hilbert spaces to the smooth Banach space setting. The proposed…

We observe that the classical notion of numerical radius gives rise to a notion of smoothness in the space of bounded linear operators on certain Banach spaces, whenever the numerical radius is a norm. We demonstrate an important class of…

This paper introduces a new definition of $\alpha$-monotone operators in real 2-uniformly convex and smooth Banach spaces. Based on this new definition, we establish several novel structural and analytical properties of such operators,…

The purpose of this note is to show that, if $\mcB$ is a uniformly convex Banach, then the dual space $\mcB'$ has a "Hilbert space representation" (defined in the paper), that makes $\mcB$ much closer to a Hilbert space then previously…

We study Birkhoff-James orthogonality of compact (bounded) linear operators between Hilbert spaces and Banach spaces. Applying the notion of semi-inner-products in normed linear spaces and some related geometric ideas, we generalize and…