Related papers: Maps completely preserving the quadratic operators

Let $\mathcal{B} (X)$ be the algebra of all bounded linear operators on an infinite-dimensional complex Banach space $X$. For an operator $ T \in \mathcal{B} (X)$, $K(T)$ denotes as usual the analytic core of $T$. We determine the form of…

Let $\mathcal{A}$ and $\mathcal{B}$ be two unital complex $\ast $-algebras such that $\mathcal{A}$ has a nontrivial projection. In this paper, we study the structure of bijective mappings $\Phi :\mathcal{A}\rightarrow \mathcal{B}$…

Let $X$, $Y$ be two real Banach spaces, and $\eps\geq0$. A map $f:X\rightarrow Y$ is said to be a standard $\eps$-isometry if $|\|f(x)-f(y)\|-\|x-y\||\leq\eps$ for all $x,y\in X$ and with $f(0)=0$. We say that a pair of Banach spaces…

A space $X$ is said to be hereditarily indecomposable if no two (infinite dimensional) subspaces of $X$ are in a direct sum. In this paper, we show that if $X$ is a complex hereditarily indecomposable Banach space, then every operator from…

Let $X$ be a separable nonquasireflexive Banach space. Let $Y$ be a Banach space isomorphic to a subspace of $X^*$. The paper is devoted to the following questions: 1. Under what conditions does there exist an isomorphic embedding $T:Y\to…

We characterise those Banach spaces $X$ which satisfy that $L(Y,X)$ is octahedral for every non-zero Banach space $Y$. They are those satisfying that, for every finite dimensional subspace $Z$, $\ell_\infty$ can be finitely-representable in…

A well-known theorem of Paulsen says that if $\mathcal{A}$ is a unital operator algebra and $\phi:\mathcal{A}\to B(\mathcal{H})$ is a unital completely bounded homomorphism, then $\phi$ is similar to a completely contractive map $\phi'$.…

A bounded linear operator $U$ between Banach spaces is universal for the complement of some operator ideal $\mathfrak{J}$ if it is a member of the complement and it factors through every element of the complement of $\mathfrak{J}$. In the…

We introduce two operators on stable configurations of the sandpile model that provide an algorithmic bijection between recurrent and parking configurations. This bijection preserves their equivalence classes with respect to the sandpile…

Let $\mathcal{H}$ be a separable complex Hilbert space. A conjugate-linear map $C:\mathcal{H}\to \mathcal{H}$ is called a conjugation if it is an involutive isometry. In this paper, we focus on the following interpolation problems: Let…

A pair of functions defined on a set X with values in a vector space E is said to be disjoint if at least one of the functions takes the value 0 at every point in X. An operator acting between vector-valued function spaces is disjointness…

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…

An operator $T \in \mathcal{B}(X)$ defined on a Banach space $X$ satisfies property $(gb)$ if the complement in the approximate point spectrum $\sigma_{a}(T)$ of the upper semi-B-Weyl spectrum $\sigma_{SBF_{+}^{-}}(T)$ coincides with the…

We show that if an infinite-dimensional Banach space X has a symmetric basis then there exists a bounded, linear operator R : X --> X such that the set A = {x in X : ||R^n(x)|| --> infinity} is non-empty and nowhere dense in X. Moreover, if…

Let $A,X,Y$ be Banach spaces and $A\times X\to Y$, $(a,x)\mapsto ax$, be a continuous bilinear function, called a *Banach action*. We say that this action *preserves unconditional convergence* if for every bounded sequence…

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…

Let $\{C_i\}_{i\in \Gamma_1},$ and $\{D_j\}_{j\in \Gamma_2},$ be two families of Cartan factors such that all of them have dimension at least $2$, and consider the atomic JBW$^*$-triples $A=\bigoplus\limits_{i\in \Gamma_1}^{\ell_{\infty}}…

We show that any multiplicative bijection between the algebras of differentiable functions, defined on differentiable manifolds of positive dimension, is an algebra isomorphism, given by composition with a unique diffeomorphism.

We show that the main problem left open in Wenzel: "Real and complex operator ideals" (wenzelopidls.latex), can be solved using the Banach spaces $Z_\alpha$ recently constructed by Kalton: "An elementary example of a Banach space not…

We consider bicolored maps, i.e. graphs which are drawn on surfaces, and construct a bijection between (i) oriented maps with arbitary face structure, and (ii) (weighted) non-oriented maps with exactly one face. Above, each non-oriented map…