Related papers: On masas of the Calkin algebra generated by projec…

Let ${\cal C}({\cal H})={\cal B}({\cal H}) / {\cal K}({\cal H})$ be the Calkin algebra (${\cal B}({\cal H})$ the algebra of bounded operators on the Hilbert space ${\cal H}$, ${\cal K}({\cal H})$ the ideal of compact operators and…

In 2007 Phillips and Weaver showed that, assuming the Continuum Hypothesis, there exists an outer automorphism of the Calkin algebra. (The Calkin algebra is the algebra of bounded operators on a separable complex Hilbert space, modulo the…

Let $K$ be a compact metric space and let $\gamma = (\gamma_1, \dots, \gamma_n)$ be a system of proper contractions on $K$. We study a C*-algebra $\mathcal{MC}_{\gamma_1, \dots, \gamma_n}$ generated by all multiplication operators by…

Let $K$ be a compact metric space and let $\varphi: K \to K$ be continuous. We study C*-algebra $\mathcal{MC}_\varphi$ generated by all multiplication operators by continuous functions on $K$ and a composition operator $C_\varphi$ induced…

Let $K$ be a compact metric space and let $\varphi: K \to K$ be continuous. We study a C*-algebra $\mathcal{MC}_\varphi$ generated by all multiplication operators by continuous functions on $K$ and a composition operator $C_\varphi$ induced…

For every Banach space $X$ with a Schauder basis consider the Banach algebra $\mathbb{R} I\oplus\mathcal{K}_\mathrm{diag}(X)$ of all diagonal operators that are of the form $\lambda I + K$. We prove that $\mathbb{R}…

In this paper we consider the question of what abelian groups can arise as the $K$-theory of $\mathrm{C}^*$-algebras arising from minimal dynamical systems. We completely characterize the $K$-theory of the crossed product of a space $X$…

We study operator semigroups in the Calkin algebra $\mathcal{Q}(\mathcal{H})$, represented as a subalgebra of the algebra of bounded linear operators on a Hilbert space via one of `canonical' Calkin's representations. Using the BDF theory,…

Maximal abelian subalgebras of one of the classical real inhomogeneous Lie algebras are constructed, namely those of the pseudoeuclidean Lie algebra e(p,q). Use is made of the semidirect sum structure of e(p,q) with the translations T(p+q)…

The maximal Abelian subalgebras of the Euclidean e(p,0) and pseudoeuclidean e(p,1)Lie algebras are classified into conjugacy classes under the action of the corresponding Lie groups E(p,0) and E(p,1), and also under the conformal groups…

We construct an essential extension of $\mathcal K(\ell_2({\mathfrak{c}}))$ by $\mathcal K(\ell_2)$, where ${\mathfrak{c}}$ denotes the cardinality of continuum, i.e., a $C^*$-algebra $\mathcal A\subseteq \mathcal B(\ell_2)$ satisfying the…

We consider the Calkin algebra $\mathcal{Q}(\ell_2)$, i.e., the quotient of the algebra $\mathcal B(\ell_2)$ of all bounded linear operators on the separable Hilbert space $\ell_2$ divided by the ideal $\mathcal K(\ell_2)$ of all compact…

We investigate C^*-algebras generated by scaling elements. We generalize the Wold decomposition and Coburn's theorem on isometries to scaling elements. We also completely determine when the C^*-algebra generated by a scaling element…

We investigate the set-theoretic properties of the lattice of projections in the Calkin algebra of a separable infinite-dimensional Hilbert space in relation to those of the Boolean algebra $P(\omega)/{\rm fin}$, which is isomorphic to the…

It is shown that if $C_1$ and $C_2$ are maximal abelian self-adjoint subalgebras (masas) of C*-algebras $A_1$ and $A_2$, respectively, then the completion $C_1\otimes C_2$ of the algebraic tensor product $C_1\odot C_2$ of $C_1$ and $C_2$ in…

In present work we deal with the class $\mathcal{C}=\mathcal{C}_1\cup \mathcal{C}_2$ where $\mathcal{C}_1$ (respectively, $\mathcal{C}_2$) is formed by all separable Uniform algebras (respectively, separable commutative C$^*$-algebras) with…

Every $\mathrm{C}^*$-algebra, regardless of its density character, can be embedded into the Calkin algebra in a forcing extension of the universe obtained without collapsing any cardinal.

We consider various quotients of the C*-algebra of bounded operators on a nonseparable Hilbert space, and prove in some cases that, consistently, there are many outer automorphisms.

A well-known result in dynamical systems asserts that any Cantor minimal system $(X,T)$ has a maximal rational equicontinuous factor $(Y,S)$ which is in fact an odometer, and realizes the rational subgroup of the $K_0$-group of $(X,T)$,…

For every well founded tree $\mathcal{T}$ having a unique root such that every non-maximal node of it has countable infinitely many immediate successors, we construct a $\mathcal{L}_\infty$-space $X_{\mathcal{T}}$. We prove that for each…