Related papers: Separable Lindenstrauss spaces whose duals lack th…

In this paper, we introduce the concept of quasi-point-separable topological vector spaces, which has the following important properties: 1.In general, the conditions for a topological vector space to be quasi-point-separable is not very…

In this paper, we explore the fixed point theory of $n$-valued maps using configuration spaces and braid groups, focussing on two fundamental problems, the Wecken property, and the computation of the Nielsen number. We show that the…

We establish common fixed point theorems for two pairs of weakly compatible self-mappings using an auxiliary function of two variables. Unlike classical results, our theorems do not assume continuity of the mappings and require completeness…

What is the correct noncommutative generalization of the functor $C_0(X) \mapsto \ell^\infty(X)$ for locally compact Hausdorff $X$ having a countable basis? Making the ansatz $K(\ell^2) \mapsto B(\ell^2)$, we expect that every unital…

Nonreflexive Banach spaces that are complemented in their bidual by an L-projection - like preduals of von Neumann algebras or the Hardy space $H^1$ - contain, roughly speaking, many copies of $l^1$ which are very close to isometric copies.…

Suppose that E is a Banach space, {\tau} a topology under which the norm of E becomes {\tau}-lower semicontinuous and S a commuting family of {\tau}-continuous nonexpansive mappings defined on a {\tau}-compact convex subset C of E: It is…

Let $(A, B)$ be a nonempty bounded closed convex proximal parallel pair in a nearly uniformly convex Banach space and $T: A\cup B \rightarrow A\cup B$ be a continuous and asymptotically relatively nonexpansive map. We prove that there…

A space X has the local fixed point property LFPP, (local periodic point property LPPP) if it has an open basis $\mathcal{B}$ such that, for each $B\in \mathcal{B}$, the closure $\overline{B}$ has the fixed (periodic) point property. Weaker…

We introduce and study the noncommutative weak Extension Principle, a lifting principle aiming to characterise $^*$-homomorphisms between coronas of nonunital separable $\mathrm{C}^*$-algebras. While this principle fails if the Continuum…

This paper provides a fixed point theorem for asymptotically nonexpansive mappings in uniformly convex hyperbolic spaces as well as new effective results on the Krasnoselski-Mann iterations of such mappings. The latter were found using…

We prove that given a locally compact Hausdorff space, $K$, and a compact C$^*$-algebra, $\mathcal{A}$, the C$^*$-algebra $C(K, \mathcal{A})$ satisfies that every convex combination of slices of the closed unit ball is relatively weakly…

We study expansive homeomorphisms of a compact metric space $X$ through the lens of the commutative $C^*$-algebra $C(X)$ of continuous complex-valued functions, viewed as observables of the system. We introduce the notion of expansive…

In this paper, we investigate the existence of fixed points for asymptotically nonexpansive mappings with center 0 defined on closed convex subsets of various Banach spaces. Three applications are given. Firstly, we prove that our results…

Motivated by results of Juh\'asz and van Mill in [13], we define the cardinal invariant $wt(X)$, the weak tightness of a topological space $X$, and show that $|X|\leq 2^{L(X)wt(X)\psi(X)}$ for any Hausdorff space $X$ (Theorem 2.8). As…

A topological space has the fixed point property if every continuous self-map of that space has at least one fixed point. We demonstrate that there are serious restraints imposed by the requirement that there be a choice of fixed points…

We show that there exist $\mathcal L_\infty$-subspaces of separable isomorphically polyhedral Lindenstrauss spaces that cannot be renormed to be a Lindenstrauss space.

The notion of a firmly nonexpansive mapping is central in fixed point theory because of attractive convergence properties for iterates and the correspondence with maximal monotone operators due to Minty. In this paper, we systematically…

We discuss basic topological properties of unitary dual spaces of nilpotent Lie groups, using some ideas from operator algebras and their noncommutative dimension theory. The general results are illustrated by many examples.

For a topological space $X$ a topological contraction on $X$ is a closed mapping $f:X\to X$ such that for every open cover of $X$ there is a positive integer $n$ such that the image of the space $X$ via the $n$th iteration of $f$ is a…

Let $X$ be a Banach space and $Y \subseteq X$ be a closed subspace. We prove that if the quotient $X/Y$ is weakly Lindel\"{o}f determined or weak Asplund, then for every $w^*$-convergent sequence $(y_n^*)_{n\in \mathbb N}$ in $Y^*$ there…