Related papers: Orthogonal forms and orthogonality preservers on r…

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 known, by Gelfand theory, that every commutative JB$^*$-triple admits a representation as a space of continuous functions of the form $$C_0^{\mathbb{T}}(L) = \{ a\in C_0(L) : a(\lambda t ) = \lambda a(t), \ \forall \lambda\in…

The purpose of this short note is to prove that if $A$ and $B$ are unital C*-algebras and $\phi : A \to B$ is a unital *-preserving ring homomorphism, then $\phi$ is contractive; i.e., $\| \phi (a) \| \leq \| a \|$ for all $a \in A$. (Note…

Let $A$ be a unital $B_{0}$-algebra with an orthogonal basis, then every multiplicative linear functional on $A$ is continuous. This gives an answer to a problem posed by Z. Sawon and Z. Wronski.

We study holomorphic maps between C$^*$-algebras $A$ and $B$. When $f:B_A (0,\varrho) \longrightarrow B$ is a holomorphic mapping whose Taylor series at zero is uniformly converging in some open unit ball $U=B_{A}(0,\delta)$ and we assume…

We establish a more precise description of those surjective or bijective continuous linear operators preserving orthogonality between C$^*$-algebras. The new description is applied to determine all uniformly continuous one-parameter…

We investigate orthonormality-preserving, C*-conformal and conformal module mappings on Hilbert C*-modules to obtain their general structure. Orthogonality-preserving bounded module maps T act as a multiplication by an element \lambda of…

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.

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…

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…

In this paper we present results concerning orthogonality in Hilbert $C^*$-modules. Moreover, for a $C^*$-algebra $\mathscr{A}$, we prove theorems concerning the multi-$\mathscr{A}$-linearity and its preservation by $\mathscr{A}$-linear…

Due to the corresponding fact concerning Hilbert spaces, it is natural to ask if the linearity and the orthogonality structure of a Hilbert $C^*$-module determine its $C^*$-algebra-valued inner product. We verify this in the case when the…

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 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…

Let $A$ be a $C^*$-algebra. Let $E$ and $F$ be Hilbert $A$-modules with $E$ being full. Suppose that $\theta : E\to F$ is a linear map preserving orthogonality, i.e., $<\theta(x), \theta(y) > = 0$ whenever $<x, y > = 0$. We show in this…

We investigate the orthogonality preserving property for pairs of mappings on inner product $C^*$-modules extending existing results for a single orthogonality-preserving mapping. Guided by the point of view that the $C^*$-valued inner…

We study Birkhoff-James orthogonality and its pointwise symmetry in commutative $C^*$ algebras, i.e., the space of all continuous functions defined on a locally compact Hausdorff space that vanish at infinity. We use this characterization…

We prove that every biorthogonality preserving linear surjection between two dual or compact C$^*$-algebras or between two von Neumann algebras is automatically continuous.

We investigate linear operators between C$^\ast$-algebras which approximately preserve involution and orthogonality, the latter meaning that for some $\varepsilon>0$ we have $\|\phi(x)\phi(y)\|\leq\varepsilon\|x\|\|y\|$ for all positive…

Let $A,B$ be C*-algebras, $B_A(0;r)$ the open ball in $A$ centered at $0$ with radius $r>0$, and $H:B_A(0;r)\to B$ an orthogonally additive holomorphic map. If $H$ is zero product preserving on positive elements in $B_A(0;r)$, we show, in…