Related papers: Biseparating maps between operator algebras

Let H be a complex Hilbert space and denote by Bs(H) the set of all self-adjoint bounded linear operators on H. In this paper we describe the form of all bijective maps (no linearity or continuity is assumed) on Bs(H) which preserve the…

In the present paper we study the structure of a Banach algebra B(A, T_g) generated by a certain Banach algebra $A$ of operators acting in a Banach space D and a group {T_g}_{g \in G} of isometries of D such that T_g A T^{-1}_g = A. We…

We examine the phenomenon when surjective algebra homomorphisms between algebras of operators on Banach spaces are automatically injective. In the first part of the paper we shall show that for certain Banach spaces $X$ the following…

In this paper, we consider representations induced by general positive and completely positive sesquilinear maps with values in ordered Banach bimodules, such as the space of trace-class operators and the spaces of bounded linear operators…

In this article, we will give a characterization of Banach bimodules over $C^*$-algebras of compact operators that arises from operator spaces as well as a characterization of (F)-Banach bundles amongst all (H)-Banach bundles over a…

In this paper we verify that the graph forms a complete invariant for Banach algebra isomorphisms of tensor algebras of graphs. For tensor algebras associated with countable directed graphs having no sinks the graph forms an invariant for…

We study two subspace systems in a separable infinite-dimensional Hilbert space up to (bounded) isomorphism. One of the main result of this paper is the following: Isomorphism classes of two subspace systems given by graphs of bounded…

For an unbounded operator $S$ on a Banach space the existence of invariant subspaces corresponding to its spectrum in the left and right half-plane is proved. The general assumption on $S$ is the uniform boundedness of the resolvent along…

We construct an example of a real Banach space whose group of surjective isometries has no uniformly continuous one-parameter semigroups, but the group of surjective isometries of its dual contains infinitely many of them. Other examples…

We study multiplication operators on the weighted Banach spaces of an infinite tree. We characterize the bounded and the compact operators, as well as determine the operator norm. In addition, we determine the spectrum of the bounded…

We show in this paper that every bijective linear isometry between the continuous section spaces of two non-square Banach bundles gives rise to a Banach bundle isomorphism. This is to support our expectation that the geometric structure of…

The main result says that every surjective isometry between two ideal Banach function spaces satisfying certain conditions can be presented as a composition of a measurable transformation of a variable and multiplication by a function.

We prove that if two path algebras with homogeneous relations are isomorphic as algebras, then they are isomorphic as graded path algebras. This extends a result by Bell and Zhang in the connected case.

Let $E$ and $F$ be Banach lattices. We show first that the disjointness preserving linear functionals separate the points of any infinite dimensional Banach lattice $E$, which shows that in this case the unbounded disjointness operators…

It is proved that isomorphisms between algebras of smooth functions on Hausdorff smooth manifolds are implemented by diffeomorphisms. It is not required that manifolds are second countable nor paracompact. This solves a problem stated by A.…

We study the dynamics induced by an $m$-linear operator. We answer a question of B\`es and Conejero showing an example of an $m$-linear hypercyclic operator acting on a Banach space. Moreover we prove the existence of $m$-linear hypercyclic…

Let \(X\) be a compact metric space and \(E\) be a Banach space. \(\lip (X, E)\) denotes the Banach space of all \(E\)-valued little Lipschitz functions on \(X\). We show that \(\lip (X, E)^{**}\) is isometrically isomorphic to Banach space…

In this paper we study sufficient conditions for an operator to have an almost-invariant half-space. As a consequence, we show that if $X$ is an infinite-dimensional complex Banach space then every operator $T\in\mathcal{L}(X)$ admits an…

The Lipschitz space of an infinite (locally-finite) graph is defined as the set of functions on the vertices of the graph such that the differences of the values between adjacent vertices remain bounded. In this paper we prove that this set…

Let $X$ and $Y$ be compact Hausdorff spaces, $E$ and $F$ be real or complex Banach spaces, and $A(X,E)$ be a subspace of $C(X,E)$. In this paper we study linear operators $S,T: A(X,E) \lo C(Y,F)$ which are jointly separating, in the sense…