Related papers: Quotients of Banach spaces with the Daugavet prope…
It is shown that if the dual of a separable Banach space has Property($K^*$) then the original space has the weak fixed point property. This is an improvement of previously results.
We give a sufficient condition for a pair of Banach spaces $(X,Y)$ to have the following property: whenever $W_1 \subseteq X$ and $W_2 \subseteq Y$ are sets such that $\{x\otimes y: \, x\in W_1, \, y\in W_2\}$ is weakly precompact in the…
It is known that, due to the fact that $L^{1, \infty}$ is not a Banach space, if $(T_j)_j$ is a sequence of bounded operators so that $$ T_j:L^1\longrightarrow L^{1, \infty}, $$ with norm less than or equal to $||T_j||$ and $\sum_j…
In this paper we investigate the property (HLUR), a generalisation of (LUR) property of a Banach space. A Banach space having the property (HLUR) is called an HLUR space. We characterise (HLUR) property with the help of known geometric…
We give a definition of coarse quotient mapping and show that several results for uniform quotient mapping also hold in the coarse setting. In particular, we prove that any Banach space that is a coarse quotient of $L_p\equiv L_p[0,1]$,…
We study Daugavet- and $\Delta$-points in Banach spaces. A norm one element $x$ is a Daugavet-point (respectively a $\Delta$-point) if in every slice of the unit ball (respectively in every slice of the unit ball containing $x$) you can…
We provide an unified approach of results of L. Dor on the complementation of the range, and of D. Alspach on the nearness from isometries, of small into isomorphisms of L1. We introduce the notion of small subspace of L1 and show lifting…
It is shown that every Banach space either contains $\ell ^1$ or it has an infinite dimensional closed subspace which is a quotient of a H.I. Banach space.Further on, $L^p(\lambda )$, $1<p<\infty $, is a quotient of a H.I Banach space.
We study Waelbroeck's category of Banach quotients after Wegner, focusing on its basic homological and functional analytic properties.
In this paper, we introduce the concept of a pseudo weakly compact operator of order $ p $ between Banach spaces. Also we study the notion of $ p $-Dunford-Pettis relatively compact property which is in "general" weaker than the…
We provide some new consequences on the Lipschitz numerical radius and index which were introduced recently. More precisely, we give some renorming results on the Lipschitz numerical index, introduce a concept of Lipschitz numerical radius…
A nonempty closed convex bounded subset $C$ of a Banach space is said to have the weak approximate fixed point property if for every continuous map $f:C\to C$ there is a sequence $\{x_n\}$ in $C$ such that $x_n-f(x_n)$ converge weakly to 0.…
A Banach space $X$ is said to have property (K) if every $w^*$-convergent sequence in $X^*$ admits a convex block subsequence which converges with respect to the Mackey topology. We study the connection of this property with strongly weakly…
In this paper we provide a far-reaching generalization of the existent results about invariant subspaces of the differentiation operator $D=\frac{\partial}{\partial t}$ on $C^\infty(0,1)$ and the Volterra operator $Vf(t)=\int_0^tf(s)ds$, on…
We study the relation between octahedral norms, Daugavet property and the size of convex combinations of slices in Banach spaces. We prove that the norm of an arbitrary Banach space is octahedral if, and only if, every convex combination of…
We investigate the minimum modulus analogue of the weak maximizing property, termed the \emph{weak minimizing property}. We establish that the pairs $(\ell_p, L^p[0, 1])$ for $2 \leq p < \infty$ and $(\ell_s \oplus_q \ell_q, \ell_r \oplus_p…
It is shown that if the Deddens algebra ${\mathcal D}_T$ associated with a quasinilpotent operator $T$ on a complex Banach space is closed and localizing then $T$ has a nontrivial closed hyperinvariant subspace.
Properties of first-order Sobolev-type spaces on abstract metric measure spaces, so-called Newtonian spaces, based on quasi-Banach function lattices are investigated. The set of all weak upper gradients of a Newtonian function is of…
An operator $G : \allowbreak X \to Y$ is said to be a Daugavet center if $\|G + T\| = \|G\| + \|T\|$ for every rank-1 operator $T : \allowbreak X \to Y$. The main result of the paper is: if $G : \allowbreak X \to Y$ is a Daugavet center,…
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…