Related papers: One-Sided Projections on C*-algebras

The purpose of this note is to describe when a general complex algebraic $^*$-algebra is pre-$C^*$-normed, and to investigate their structure when the $^*$-algebras are Baer $^*$-rings in addition to algebraicity. As a main result we prove…

Halmos' two projections theorem for Hilbert space operators is one of the fundamental results in operator theory. In this paper, we introduce the term of two harmonious projections in the context of adjointable operators on Hilbert…

Let $X_1, \ldots, X_n,Y$ be classes of Banach spaces-valued sequences. An $n$-linear operator $A$ between Banach spaces belongs to the ideal of $(X_1, \ldots, X_n;Y)$-summing multilinear operators if $(A(x_j^1, \ldots, x_j^n))_{j=1}^\infty$…

Let $X$ be a locally compact non compact Hausdorff topological space. Consider the algebras $C(X)$, $C_b(X)$, $C_0(X)$, and $C_{00}(X)$ of respectively arbitrary, bounded, vanishing at infinity, and compactly supported continuous functions…

The article is devoted to quasilinear operators in spaces over quaternions and octonions. Spectral theory of bounded and unbounded operators is investigated. Analogs of C^* algebras are defined and studied. Among main results are analogs of…

In the current paper, we generalize the "compact operator" part of the Voiculescu's non-commutative Weyl-von Neumann theorem on approximate equivalence of unital $*$-homomorphisms of an commutative C$^*$ algebra $\mathcal{A}$ into a…

Let $A$ be a unital $C^*$-algebra containing a closed two-sided ideal $J$ and an operator system $X$. We enlarge $X$ to an operator system $\mathcal{S}(X,J)$ in $\mathbb{M}_2(A)$, and show that in order for $\mathcal{S}(X,J)$ to be…

We consider various lifting problems for C*-algebras. As an application of our results we show that any commuting family of order zero maps from matrices to a von Neumann central sequence algebra can be lifted to a commuting family of order…

Let G be a locally compact group. Consider the Banach algebra L_1(G)^**, equipped with the first Arens multiplication, as well as the algebra LUC(G)^*, the dual of the space of bounded left uniformly continuous functions on G, whose product…

In this paper, for a Banach algebra A, we introduced the new notions of approximately left $\phi$-biprojective and approximately left character biprojective, where $\phi$ is a non-zero multiplicative linear functional on A. We show that for…

We generalize an important class of Banach spaces, namely the $M$-embedded Banach spaces, to the non-commutative setting of operator spaces. The one-sided $M$-embedded operator spaces are the operator spaces which are one-sided $M$-ideals…

We give an equivalence of categories between: (i) M\"obius vertex algebras which are equipped with a choice of generating family of quasiprimary vectors, and (ii) (not-necessarily-unitary) M\"obius-covariant Wightman conformal field…

We show that semiprojectivity of a C*-algebra is preserved when passing to C*-subalgebras of finite codimension. In particular, any pullback of two semiprojective C*-algebras over a finite-dimensional C*-algebra is again semiprojective.

Let $\mathcal{M}$ be a von Neumann algebra equipped with a faithful normal semi-finite trace $\tau$ and let $S_0(\tau)$ be the algebra of all $\tau$-compact operators affiliated with $\mathcal{M}$. Let $E(\tau)\subseteq S_0(\tau)$ be a…

We review and analyse techniques from the literature for extending a normed algebra, A to a normed algebra, B, so that B has interesting or desirable properties which A may lack. For example, B might include roots of monic polynomials over…

For a Hecke pair $(G, H)$ and a finite-dimensional representation $\sigma$ of $H$ on $V_\sigma$ with finite range we consider a generalised Hecke algebra $\H_\sigma(G, H)$, which we study by embedding the given Hecke pair in a Schlichting…

Let X be a compact Hausdorf space, let A be a commutative unital Banach algebra, and let C(X,A) denote the algebra of continuous A-valued functions on $X$ equipped with the uniform norm ||f||=sup{||f(x)||:x\in X} for all f in C(X,A).…

We characterize the modules of infinite projective dimension over the endomorphism algebras of Opperman-Thomas cluster tilting objects $X$ in $(n+2)$-angulated categories $(\mathcal C,\Sigma^n,\Theta)$. For an indecomposable object $M$ of…

H. Dye defined the projections $P_{i,j}(a)$ of a $C^*$-matrix algebra by {eqnarray*} P_{i,j}(a) &=& (1+aa^*)^{-1}\otimes E_{i,i} + (1+aa^*)^{-1}a \otimes E_{i,j} + a^*(1+aa^*)^{-1} \otimes E_{j,i} + a^*(1+aa^*)^{-1}a\otimes E_{j,j},…

This paper is a revision and an enlargement of the previous version titled "Extreme points of the unit ball of a quasi-multiplier space" which had been circulated since 2004. We study extreme points of the unit ball of an operator space by…