Related papers: Universally reversible JC*-triples and operator sp…

The characteristic function has been an important tool for studying completely non unitary contractions on Hilbert spaces. In this note, we consider completely non-coisometric contractive tuples of commuting operators on a Hilbert space…

We generalize the notion of a continuous field of C*-algebras to that of Hilbert C*-bimodules. Given a partially ordered set $P$ and a monotonically non-decreasing family of ternary rings of operators (TROs) assigned to the points of $P$,…

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…

Can there be a structure space-type theory for an arbitrary class of ideals of a ring? The ideal spaces introduced in this paper allows such a study and our theory includes (but not restricted to) prime, maximal, minimal prime, strongly…

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 prove that the predual, $M_*$, of a JBW$^*$-triple $M$ is a 1-Plichko space (i.e. it admits a countably 1-norming Markushevich basis or, equivalently, it has a commutative 1-projectional skeleton), and obtain a natural description of the…

We improve known perturbation results for self-adjoint operators in Hilbert spaces and prove spectral enclosures for diagonally dominant $J$-self-adjoint operator matrices. These are used in the proof of the central result, a perturbation…

We give an order-theoretic characterization of the essential image of the forgetful functor from the category of real/complex unital C*-algebras to the category of real/complex unital operator systems. It is based on the characterization of…

Given Hilbert space operators $P,T\in B(\H), P\geq 0$ invertible, $T$ is $(m,P)-$ expansive (resp., $(m,P)-$ isometric) for some positive integer $m$ if…

We show that a separable purely infinite C*-algebra is of real rank zero if and only if its primitive ideal space has a basis consisting of compact-open sets and the natural map K_0(I) -> K_0(I/J) is surjective for all closed two-sided…

We generalize a preceding simple proof of the Jamiolkowski criterion to check whether a given linear map between algebras of operators is completely positive or not. The generalization is performed to embrace all algebras of Hilbert-Schmidt…

For H a separable infinite dimensional complex Hilbert space, we prove that every B(H) operator has a basis with respect to which its matrix representation has a universal block tridiagonal form with block sizes given by a simple…

We study the spectral properties of positive absolutely minimum attaining operators defined on infinite dimensional complex Hilbert spaces and using that derive a characterization theorem for such type of operators. We construct several…

We prove that, given a constant $K> 2$ and a bounded linear operator $T$ from a JB$^*$-triple $E$ into a complex Hilbert space $H$, there exists a norm-one functional $\psi\in E^*$ satisfying $$\|T(x)\| \leq K \, \|T\| \, \|x\|_{\psi},$$…

Normality of bounded and unbounded adjointable operators are discussed. Suppose $T$ is an adjointable operator between Hilbert C*-modules which has polar decomposition, then $T$ is normal if and only if there exists a unitary operator $…

Let $\mathcal{H}$ be a complex, separable Hilbert space, and $\mathcal{B}(\mathcal{H})$ denote the set of all bounded linear operators on $\mathcal{H}$. Given an orthogonal projection $P \in \mathcal{B}(\mathcal{H})$ and an operator $D \in…

We describe and characterize the contractively decomposable projections on noncommutative $\mathrm{L}^p$-spaces. Our result relies on a new lifting result for decomposable maps of independent interest and on some tools from ergodic theory.…

We investigate $\rho$-orthogonality and its local symmetry in the space of bounded linear operators. A characterization of Hilbert space operators with symmetric numerical range is established in terms of $\rho$-orthogonality. Further, we…

We define a tracelike transformation to be a natural family of conjugation invariant maps $T_{x,C}: hom_C(x,x) \to hom_C(1,1)$ for all dualisable objects $x$ in any symmetric monoidal infinity-category $C$. This generalises the trace from…

Jordan operator algebras are norm-closed spaces of operators on a Hilbert space with $a^2 \in A$ for all $a \in A$. We study noncommutative topology, noncommutative peak sets and peak interpolation, and hereditary subalgebras of Jordan…