Related papers: Contractive projections and real positive maps on …
We describe all isometries of the $q$-numerical radius on the space ${\mathcal K}(\mathcal H)$ of compact operators on a (possibly infinite-dimensional) Hilbert space $\mathcal H$.
One approach to multivariate operator theory involves concepts and techniques from algebraic and complex geometry and is formulated in terms of Hilbert modules. In these notes we provide an introduction to this approach including many…
We extend the $\lambda$-theory of operator spaces given by Defant and Wiesner (2014), that generalizes the notion of the projective, Haagerup and Schur tensor norm for operator spaces to matrix ordered spaces and Banach $*$-algebras. Given…
In this paper the authors seek to trace in an accessible fashion the rapid recent development of the theory of the matrix geometric mean in the cone of positive definite matrices up through the closely related operator geometric mean in the…
We show that if $T$ is an isometry (as metric spaces) between the invertible groups of unital Banach algebras, then $T$ is extended to a surjective real-linear isometry up to translation between the two Banach algebras. Furthermore if the…
In recent work of the second author, a technical result was proved establishing a bijective correspondence between certain open projections in a C*-algebra containing an operator algebra A, and certain one-sided ideals of A. Here we give…
We generalize some facts about function algebras to operator algebras, using the `noncommutative Shilov boundary' or $C^*$-envelope first considered by Arveson. In the first part we study and characterize complete isometries between…
Hilbert C*-modules are the analogues of Hilbert spaces where a C*-algebra plays the role of the scalar field. With the advent of Kasparov's celebrated KK-theory they became a standard tool in the theory of operator algebras. While the…
The main purpose of this paper is, in the general setting of the adjointable operators on Hilbert $C^*$-modules, to develop two new tools that can be applied to deal with the positive solutions of certain operator equations, the operator…
In this paper we completely characterize the norm attainment set of a bounded linear operator on a Hilbert space. This partially answers a question raised recently in [\textit{D. Sain, On the norm attainment set of a bounded linear…
The following topics are presented in these notes: Elements of Banach algebras, Banach algebras of the form $L^1(G)$, where $G$ is a locally compact group, spectrum of elements of Banach algebras, the spectral theory of compact operators on…
We define a strong Morita-type equivalence $\sim _{\sigma \Delta }$ for operator algebras. We prove that $A\sim _{\sigma \Delta }B$ if and only if $A$ and $B$ are stably isomorphic. We also define a relation $\subset _{\sigma \Delta }$ for…
The aim of this paper is to show that between standard operator algebras every bijective map with a certain multiplicativity property related to Jordan triple isomorphisms of associative rings is automatically additive.
An operator system modulo the kernel of a completely positive linear map of the operator system gives rise to an operator system quotient. In this paper, operator system quotients and quotient maps of certain matrix algebras are considered.…
Functional analysis, especially the theory of Hilbert spaces and of operators on these, form an important area in mathematics. We formalized the Isabelle/HOL library Complex_Bounded_Operators containing a large amount of theorems about…
We consider abstract Banach spaces of analytic functions on general bounded domains that satisfy only a minimum number of axioms. We describe all invertible (equivalently, surjective) weighted composition operators acting on such spaces.…
The purpose of this article is to introduce projective geometry over composition algebras : the equivalent of projective spaces and Grassmannians over them are defined. It will follow from this definition that the projective spaces are in…
In this note I discuss some aspects of a formulation of quantum mechanics based entirely on the Jordan algebra of observables. After reviewing some facts of the formulation in the \CS -approach I present a Jordan-algebraic Hilbert space…
This article presents an isomorphism between two operator algebras $L_1$ and $L_2$ where $L_1$ is the set of operators on a space of Hilbert-Schmidt operators and $L_2$ is the set of operators on a tensor product space. We next compare our…
We study operator spaces, operator algebras, and operator modules, from the point of view of the `noncommutative Shilov boundary'. In this attempt to utilize some `noncommutative Choquet theory', we find that Hilbert C$^*-$modules and their…