Related papers: Gateaux derivative of C* norm

We revisit the construction of signature classes in C*-algebra K-theory, and develop a variation that allows us to prove equality of signature classes in some situations involving homotopy equivalences of noncompact manifolds that are only…

In the first part of the paper, we use states on $C^*$-algebras in order to establish some equivalent statements to equality in the triangle inequality, as well as to the parallelogram identity for elements of a pre-Hilbert $C^*$-module. We…

We introduce a notion of ellipticity of complexes of linear pseudodifferential operators acting on sections of $A$-Hilbert bundles over smooth manifolds, $A$ being a $C^*$-algebra. We prove that the cohomology groups of an $A$-elliptic…

There are two notions of approximate Birkhoff-James orthogonality in a normed space. We characterize both the notions of approximate Birkhoff-James orthogonality in the space of bounded linear operators defined on a normed space. A complete…

We study Birkhoff-James orthogonality of compact (bounded) linear operators between Hilbert spaces and Banach spaces. Applying the notion of semi-inner-products in normed linear spaces and some related geometric ideas, we generalize and…

The construction of a C*-algebra of a differential groupoid is presented. It is shown that it defines a covariant functor from the category of differential groupoids in a sense of S. Zakrzewski to the category of C*-algebras.

Let us consider the set S^A(\R^n) of rapidly decreasing functions G:\R^n \to A, where A is a separable C^*-algebra. We prove a version of the Calder\'on-Vaillancourt theorem for pseudodifferential operators acting on S^A(\R^n) whose symbol…

The main result of the paper is an extension of the Dirichlet problem from (closures of) bounded open domains U to arbitrary compact subsets X of the complex plane, i.e. the closure of the corresponding space of functions which are harmonic…

Let $G$ be a semi-simple real Lie group of real rank one and $\Gamma$ be a discrete subgroup in $G$ such that $\Gamma \backslash G$ has finite volume. We introduce a new group $C^*$-algebra $C^*_r(G, \Gamma)$, which provides a natural…

Given any irreducible inclusion $\mB \subset \mA$ of unital $C^*$-algebras with a finite-index conditional expectation $E: \mA \to \mB$, we show that the set of $E$-compatible intermediate $C^*$-subalgebras is finite, thereby generalizing a…

Let $\mathscr{M}$ be a von Neumann algebra and $a$ be a self-adjoint operator affiliated with $\mathscr{M}$. We define the notion of an "integral symmetrically normed ideal" of $\mathscr{M}$ and introduce a space $OC^{[k]}(\mathbb{R})…

The classical Gelfand--Naimark theorems provide important insight into the structure of general and of commutative C*-algebras. It is shown that these can be generalized to certain ordered *-algebras. More precisely, for $\sigma$-bounded…

Let $\alpha : \Gamma \curvearrowright A$ be an action of a discrete group $\Gamma$ on a unital C*-algebra $A$ by *-automorphisms and let $A \rtimes_{\alpha,\lambda} \Gamma$ denote the corresponding reduced crossed product C*-algebra.…

Assuming a unitarily invariant norm $|||\cdot|||$ is given on a two-sided ideal of bounded linear operators acting on a separable Hilbert space, it induces some unitarily invariant norms $|||\cdot|||$ on matrix algebras $\mathcal{M}_n$ for…

The functional calculus for normal elements in $C^*$-algebras is an important tool of analysis. We consider polynomials $p(a,a^*)$ for elements $a$ with small self-commutator norm $\|[a,a^*]\| \le \delta$ and show that many properties of…

Let $R$ be a rational function. The iterations $(R^n)_n$ of $R$ gives a complex dynamical system on the Riemann sphere. We associate a $C^*$-algebra and study a relation between the $C^*$-algebra and the original complex dynamical system.…

Let $\mathcal{L}(\mathscr{H})$ denote the $C^*$-algebra of adjointable operators on a Hilbert $C^*$-module $\mathscr{H}$. We introduce the generalized Cauchy-Schwarz inequality for operators in $\mathcal{L}(\mathscr{H})$ and investigate…

C*-algebras are widely used in mathematical physics to represent the observables of physical systems, and are sometimes taken as the starting point for rigorous formulations of quantum mechanics and classical statistical mechanics.…

We present a geometric approach to defining an algebra $\hat{\mathcal G}(M)$ (the Colombeau algebra) of generalized functions on a smooth manifold $M$ containing the space ${\mathcal D}'(M)$ of distributions on $M$. Based on differential…

We introduce certain $C^*$-algebras and $k$-graphs associated to $k$ finite dimensional unitary representations $\rho_1,...,\rho_k$ of a compact group $G$. We define a higher rank Doplicher-Roberts algebra $\mathcal{O}_{\rho_1,...,\rho_k}$,…