Related papers: Automatic continuity of biorthogonality preservers…

We prove that every biorthogonality preserving linear surjection from a weakly compact JB$^*$triple containing no infinite dimensional rank-one summands onto another JB$^*$-triple is automatically continuous. We also show that every…

In 2014, we determine the precise form of a continuous orthogonal form on a commutative real C$^*$-algebra. We also describe the general form of a (not-necessarily continuous) orthogonality preserving linear map between commutative unital…

It is shown that every linear strong Birkhoff-James isomorphism between unital $C^*$-algebras is a $*$-isomorphism followed by a unitary multiplication. Moreover, as a partial extension of this result to the non-unital case, the form of…

We prove that every weak-local derivation on a C$^*$-algebra is continuous, and the same conclusion remains valid for weak$^*$-local derivations on von Neumann algebras. We further show that weak-local derivations on C$^*$-algebras and…

We introduce $n$-orthogonality (and completely orthogonality) preserving operators between C$^*$-algebras. Our main theorem states that every completely orthogonality preserving bounded linear mapping between C$^*$-algebras is a weighted…

We survey the results on linear local and 2-local homomorphisms and zero products preserving operators between C$^*$-algebras, and we incorporate some new precise observations and results to prove that every bounded linear 2-local…

We prove that von Neumann algebras and separable nuclear $C^*$-algebras are stable for the Banach-Mazur cb-distance. A technical step is to show that unital almost completely isometric maps between $C^*$-algebras are almost multiplicative…

We show that any homomorphism from the homeomorphism group of a compact 2-manifold, with the compact-open topology, or equivalently, with the topology of uniform convergence, into a separable topological group is automatically continuous.

Let $A$ be a $C^*$-algebra. We say that $A$ satisfies the SP if every bounded homomorphism $A\to B(K)$, with $K$ a Hilbert space, is similar to a $*$-homomorphism. We introduce three hypotheses that relate to extending hyperreflexive…

Let A be a C*-algebra and d from A into A** be a continuous linear map. We assume that d acts like derivation or anti-derivation at orthogonal elements for several types of orthogonality conditions such as ab=0, ab*=0, ab=ba=0 and…

We initiate the study of orthogonal forms on a real C$^*$-algebra. Motivated by previous contributions, due to Ylinen, Jajte, Paszkiewicz and Goldstein, we prove that for every continuous orthogonal form $V$ on a commutative real…

We prove constructive versions of various usual results related to the Gelfand duality. Namely, that the constructive Gelfand duality extend to a duality between commutative nonunital C*-algebras and locally compact completely regular…

In this paper we introduce the M\"obius disjointness for C$^*$-algebras with their automorphisms and studied the M\"obius disjointness for finite dimensional C$^*$ algebras, finite von Neumann algebras, reduced free group algebra and…

Universal continuous calculi are defined and it is shown that for every finite tuple of pairwise commuting Hermitian elements of a Su*-algebra (an ordered *-algebra that is symmetric, i.e. "strictly" positive elements are invertible, and…

It is shown that the spectral radius is continuous on a $C^*$-algebra if and only if the $C^*$-algebra is type I. This answers a question of V. Shulman and Yu.~Turovskii [10]. It is shown also that the closure of nilpotents in a…

It is established that every (not necessarily linear) 2-local $^*$-homomorphism from a von Neumann algebra into a C$^*$-algebra is linear and a $^*$-homomorphism. In the setting of (not necessarily linear) 2-local $^*$-homomorphism from a…

Let $A$ be a $C^*$-algebra acting on a Hilbert space $H$, $\sigma:A\to B(H)$ be a linear mapping and $d:A\to B(H)$ be a $\sigma$-derivation. Generalizing the celebrated theorem of Sakai, we prove that if $\sigma$ is a continuous $*$-mapping…

It is shown that every linear surjective isometry between two right, full, Hilbert C*-modules is a sum of two maps : a (bi-) module map (which is completely isometric and preserves the inner product) and a map that reverses the (bi-) module…

We define continuous C*-algebras over a topological space X and establish some basic results. If X is a locally compact Hausdorff space, continuous C*-algebras over X are equivalent to ordinary continuous C_0(X)-algebras. The main purpose…

We classify bijective maps which strongly preserve Birkhoff-James orthogonality on a finite-dimensional complex $C^*$-algebra. It is shown that those maps are close to being real-linear isometries whose structure is also determined.