Related papers: Invertible positive maps that are not automorphism

The full description of the set of positive maps $T: \qA \to \cB(\cH)$ ($\qA$ a $C^*$-algebra) is given. The approach is based on the simple prescription for selecting various types of positive maps. This prescription stems from the…

A complex compact surface which carries an automorphism of positive topological entropy has been proved by Cantat to be either a torus, a K3 surface, an Enriques surface or a rational surface. Automorphisms of rational surfaces are quite…

Let $A$ be a Banach algebra admitting a bounded approximate unit and satisfying property $\mathbb{B}$. Suppose $T: A \rightarrow X$ is a continuous linear map, where $X$ is an essential Banach $A$-bimodule. We prove that the following…

Let $X$ be a locally symmetric space $\Gamma\backslash G/K$ where $G$ is a connected non-compact semisimple real Lie group with trivial centre, $K$ is a maximal compact subgroup of $G$, and $\Gamma\subset G$ is a torsion-free irreducible…

We construct a locally finite graph and a bounded geometry metric space which do not admit a quasi-isometric embedding into any uniformly convex Banach space. Connections with the geometry of $c_0$ and superreflexivity are discussed.

We examine maps between noncommutative projective spaces. A surjection of graded rings A-->A/J induces a closed immersion Proj(A/J)-->Proj(A). A homomorphism f:A-->B between graded rings induces an affine map U --> Proj(A) from a non-empty…

A convex subset X of a linear topological space is called compactly convex if there is a continuous compact-valued map $\Phi:X\to exp(X)$ such that $[x,y]\subset\Phi(x)\cup \Phi(y)$ for all $x,y\in X$. We prove that each convex subset of…

Let $\cK$ and $\cH$ be finite dimensional Hilbert spaces and let $\fP$ denote the cone of all positive linear maps acting from $\fB(\cK)$ into $\fB(\cH)$. We show that each map of the form $\phi(X)=AXA^*$ or $\phi(X)=AX^TA^*$ is an exposed…

Assume that $X$ is a complex separable infinite dimensional Banach space and $\mathcal{B}(X)$ denotes the Banach algebra of all bounded linear operators from $X$ to itself. In 1970, P.R. Halmos raised ten open problems in Hilbert spaces.…

In this article, we study the relative negative K-groups $K_{-n}(f)$ of a map $f: X \to S $ of schemes. We prove a relative version of the Weibel conjecture i.e. if $f: X \to S$ is a smooth affine map of noetherian schemes with $\dim S=d$…

We show that any bounded operator $T$ on a separable, reflexive, infinite-dimensional Banach space $X$ admits a rank one perturbation which has an invariant subspace of infinite dimension and codimension. In the non-reflexive spaces, we…

Let $X$ be a two-sided subshift on a finite alphabet endowed with a mixing probability measure which is positive on all cylinders in $X$. We show that there exist arbitrarily small finite overlapping union of shifted cylinders which…

We present norm criteria for the existence of anti-automorphisms, as well as explicit constructions of anti-automorphisms, both on cyclic and generalized cyclic algebras. Our approach describes anti-automorphisms as polynomial maps and…

We prove that every complete connected immersed surface with positive extrinsic curvature $K$ in $H^2\times R$ must be properly embedded, homeomorphic to a sphere or a plane and, in the latter case, study the behavior of the end. Then, we…

This paper investigates topological reconstruction, related to the reconstruction conjecture in graph theory. We ask whether the homeomorphism types of subspaces of a space $X$ which are obtained by deleting singletons determine $X$…

The deck of a topological space $X$ is the set $\mathcal{D}(X)=\{[X \setminus \{x\}] \colon x \in X\}$, where $[Z]$ denotes the homeomorphism class of $Z$. A space $X$ is topologically reconstructible if whenever…

Let $G$ be a cyclic $p$-group or generalized quaternion group, $X\in \pi_0 S_G$ be a virtual $G$-set, and $V$ be a fixed point free complex $G$-representation. Under conditions depending on the sizes of $G$, $X$, and $V$, we construct a…

Let $X$ be a real Banach lattice with a unit, let $Y \subseteq X$ be a closed subspace containing the unit. In this paper we study the order theoretic (also isometric) structure of $Y$ that it may inherit from $X$ under some additional…

The paper alluded to in the title contains the following striking result: Let $I$ be the unit interval and $\Delta$ the Cantor set. If $X$ is a quasi Banach space containing no copy of $c_0$ which is isomorphic to a closed subspace of a…

We study some questions concerning the structure of the set of spreading models of a separable infinite-dimensional Banach space $X$. In particular we give an example of a reflexive $X$ so that all spreading models of $X$ contain $\ell_1$…