相关论文: One-Sided Projections on C*-algebras

We develop some tools for manipulating and constructing projections in C*-algebras. These are then applied to give short proofs of some standard projection homotopy results, as well as strengthen some fundamental classical results for…

Blecher and Read have recently introduced and studied a new notion of positivity in operator algebras, with an eye to extending certain $C^*$-algebraic results and theories to more general algebras. In the present paper we generalize some…

Let $\mathcal{M}$ be a type ${\rm II_1}$ factor and let $\tau$ be the faithful normal tracial state on $\mathcal{M}$. In this paper, we prove that given an $X \in \mathcal{M}$, $X=X^*$, then there is a decomposition of the identity into $N…

This is a complement to our previous paper on the arxiv on quantum expanders and geometry of operator spaces. We show that there is a non-exact $C^*$-algebra that is 1-subexponential, and we give several other complements to the results of…

For a long time, practitioners of the art of operator algebras always worked over the complex numbers, and nobody paid much attention to real C*-algebras. Over the last thirty years, that situation has changed, and it's become apparent that…

We show that a number of naturally occurring comparison relations on positive elements in a C*-algebra are equivalent to natural comparison properties of their corresponding open projections in the bidual of the C*-algebra. In particular we…

Based on the projective matrix spaces studied by B. Schwarz and A. Zaks, we study the notion of projective space associated to a C*-algebra A with a fixed projection p. The resulting space P(p) admits a rich geometrical structure as a…

We construct a Banach space $Z$ such that the lattice of closed two-sided ideals of the Banach algebra $\mathscr{B}(Z)$ of bounded operators on $Z$ is as follows: $$ \{0\}\subset \mathscr{K}(Z)\subset\mathscr{E}(Z) \raisebox{-.5ex}%…

Most of this article is an expanded version of our conference talk. It is essentially a survey, but some part, like most of the lengthy Section 5, is comprised of new results whose proofs are unpublished elsewhere. We begin by reviewing the…

In this short note, we prove that for a $C^*$-algebra $\aa$ generated by $n$ elements, $M_{k}(\tilde{\aa})$ is generated by $k$ mutually unitarily equivalent and almost mutually orthogonal projections for any $k\ge…

In this paper we introduce a new technique for proving norm inequalities in operator ideals with an unitarily invariant norm. Among the well known inequalities which can be proved with this technique are the L\"owner-Heinz inequality,…

We prove that a subspace of a real JBW$^*$-triple is an $M$-summand if and only if it is a weak$^*$-closed triple ideal. As a consequence, $M$-ideals of real JB$^*$-triples correspond to norm-closed triple ideals. As in the setting of…

We prove several results concerning the representation of projections on arbitrary Banach spaces. We also give illustrative examples including an example of a generalized bi-circular projection which can not be written as the average of the…

We initiate the study of annihilators in C*-algebras, showing that they are, in many ways, the best C*-algebra analogs of projections in von Neumann algebras. Using them, we obtain a type decomposition for arbitrary C*-algebras that is…

An algebra is said to be quasi-directly finite when any left-invertible element in its unitization is automatically right-invertible. It is an old observation of Kaplansky that the von Neumann algebra of a discrete group has this property;…

We study projections in the bidual of a $C^*$-algebra $B$ that are null with respect to a subalgebra $A$, that is projections $p\in B^{**}$ satisfying $|\phi|(p)=0$ for every $\phi\in B^*$ annihilating $A$. In the separable case, $A$-null…

An important result in real algebraic geometry is the projection theorem: every projection of a semialgebraic set is again semialgebraic. This theorem and some of its conclusions lie at the basis of many other results, for example the…

For a Banach D-bimodule M over an abelian unital C*-algebra D, we define E(M) as the collection of norm-one eigenvectors for the dual action of D on the Banach space dual of M. Equip E(M) with the weak-* topology. We develop general…

Let $M$ be a type I von Neumann algebra with the center $Z,$ a faithful normal semi-finite trace $\tau.$ Let $L(M, \tau)$ be the algebra of all $\tau$-measurable operators affiliated with $M$ and let $S_0(M, \tau)$ be the subalgebra in…

In this article, we use Exel's construction to associate a C*-algebra to every shift space. We show that it has the C*-algebra defined in [Carlsen and Matsumoto: Some remarks on the C*-algebras associated with subshifts] as a quotient, and…