Operator algebras with contractive approximate identities: A large operator algebra in $c_0$

One-sided Ideals and Approximate Identities in Operator Algebras

A left ideal of any C∗-algebra is an example of an operator algebra with a right contractive approximate identity (r.c.a.i.). Indeed, left ideals in C∗-algebras may be characterized as the class of such operator algebras, which happen also to be triple systems. Conversely, we show here and in a sequel to this paper, that operator algebras with r.c.a.i. should be studied in terms of a certain le...

Closed Projections and Approximate Identities for Operator Algebras

Let A be a (not necessarily selfadjoint) subalgebra of a unital C-algebra B which contains the unit of B. The right ideals of A with left contractive approximate identity are characterized as those subspaces of A supported by the orthogonal complement of a closed projection in B which also lies in A. Although this seems quite natural, the nonselfadjointness requires us to develop some interpola...

Images of contractive projections on operator algebras

It is shown that if P is a weak∗-continuous contractive projection on a JBW∗-triple M , then P(M) is of type I or semifinite, respectively, if M is of the corresponding type. We also show that P(M) has no infinite spin part if M is a type I von Neumann algebra.  2002 Elsevier Science (USA). All rights reserved.

Operator Theory and Operator Algebras

On Some Operator Identities and Representations of Algebras

Certain infinite families of operator identities related to powers of positive root generators of (super) Lie algebras of first-order differential operators and q-deformed algebras of first-order finite-difference operators are presented. 1. The following operator identity holds (J n ) n+1 ≡ (x∂x − nx) n+1 = x∂ x , ∂x ≡ d dx , n = 0, 1, 2, . . . (1) The proof is straightforward: (i) the operato...