Related papers: On stable maps of operator algebras

For a closed densely defined operator $T$ from a Hilbert space $\mathfrak{H}$ to a Hilbert space $\mathfrak{K}$, necessary and sufficient conditions are established for the factorization of $T$ with a bounded nonnegative operator $X$ on…

We present some general theorems about operator algebras that are algebras of functions on sets, including theories of local algebras, residually finite dimensional operator algebras and algebras that can be represented as the scalar…

We study operator algebraic and function theoretic aspects of algebras of bounded nc functions on subvarieties of the nc domain determined by all levels of the unit ball of an operator space (nc operator balls). Our main result is the…

We consider two twisted actions of a countable discrete group on $\sigma$-unital $C^*$-algebras. Then by taking the reduced crossed products, we get two inclusions of $C^*$-algebras. We suppose that they are strongly Morita equivalent as…

We consider projectivity and injectivity of Hilbert C*-modules in the categories of Hilbert C*-(bi-)modules over a fixed C*-algebra of coefficients (and another fixed C*-algebra represented as bounded module operators) and bounded…

We prove the $K$-theoretic Farrell-Jones conjecture for groups as in the title with coefficient rings and $C^*$-algebras which are stable with respect to compact operators. We use this and Higson-Kasparov's result that the Baum-Connes…

This paper is devoted to local derivations on subalgebras on the algebra $S(M, \tau)$ of all $\tau$-measurable operators affiliated with a von Neumann algebra $M$ without abelian summands and with a faithful normal semi-finite trace $\tau.$…

We look at various forms of spectrum and associated pseudospectrum that can be defined for noncommuting $d$-tuples of Hermitian elements of a $C^*$-algebra. The emphasis is on theoretical calculations of examples, in particular for…

Let $E$ and $F$ be Hilbert $C^*$-modules over a $C^*$-algebra $\CAlg{A}$. New classes of (possibly unbounded) operators $t:E\to F$ are introduced and investigated. Instead of the density of the domain $\Def(t)$ we only assume that $t$ is…

We study adjointable, bounded operators on the direct sum of two copies of the standard Hilbert C*-module over a unital C*-algebra A that are given by upper triangular 2 by 2 operator matrices. Using the definition of A-Fredholm and…

We show that a compact operator $A$ is a multiple of a positive semi-definite operator if and only if $$ \sigma(AB) \subseteq \overline{W(A)W(B)}, \quad\text{for all (rank one) operators $B$}. $$ An example of a normal operator is given to…

Let $G$ and $H$ be Hausdorff ample groupoids and let $R$ be a commutative unital ring. We show that if $G$ and $H$ are equivalent in the sense of Muhly-Renault-Williams, then the associated Steinberg algebras of locally constant $R$-valued…

We study lifting problems for operator semigroups in the Calkin algebra $\mathscr{Q}(\mathcal{H})$, our approach being mainly based on the Brown--Douglas--Fillmore theory. With any normal $C_0$-semigroup $(q(t))_{t\geq 0}$ in…

For each $\alpha \in (0,1)$, $A_\alpha$ denotes the universal $C^*$-algebra generated by two unitaries $u$ and $v$, which satisfy the commutation relation $uv=\exp (2\pi i\alpha)vu$. We consider the order four automorphism $\sigma$ of…

Motivated by deformation quantization, we introduced in an earlier work the notion of formal Morita equivalence in the category of $^*$-algebras over a ring $\ring C$ which is the quadratic extension by $\im$ of an ordered ring $\ring R$.…

We prove that an operator system $\mathcal S$ is nuclear in the category of operator systems if and only if there exist nets of unital completely positive maps $\phi_\lambda : \cl S \to M_{n_\lambda}$ and $\psi_\lambda : M_{n_\lambda} \to…

In this note we address the continuity of strongly singular Calder\'on-Zygmund operators on Hardy-Morrey spaces $\mathcal{HM}_{q}^{\lambda}(\mathbb{R}^n)$, assuming weaker integral conditions on the associated kernel. Important examples…

The symmetric homology of a unital algebra $A$ over a commutative ground ring $k$ is defined using derived functors and the symmetric bar construction of Fiedorowicz. For a group ring $A = k[\Gamma]$, the symmetric homology is related to…

This paper introduces the notion of Rota-Baxter $C^{\ast}$-algebras. Here a Rota-Baxter $C^{\ast}$-algebra is a $C^{\ast}$-algebra with a Rota-Baxter operator. Symmetric Rota-Baxter operators, as special cases of Rota-Baxter operators on…

Let G and K be groupoids. We present the notion of a (G_{\alpha},K_{\beta})-set and we prove a duality theorem in this context, which extends the duality theorem for graded algebras by groups. For A a unital G-graded algebra and X a finite…