On bounded and unbounded idempotents whose sum is a multiple of the identity

Unbounded expectations to some von Neumann algebras

For any injective von Neumann algebra R and any discrete, countable group G, which acts by *-automorphisms on R, we construct an idempotent mapping of an ultra-weakly dense subspace of B(H) onto the reducerd crossed product von Neumann algebra, such that it is R-bimodular and satisfies some nice relations with respect to positivity. In the case of an amenable group our unbounded expectation turns into a usual conditional expectation of norm 1.

Separability Idempotents and Multiplier Algebras

Consider two non-degenerate algebras B and C over the complex numbers. We study a certain class of idempotent elements E in the multiplier algebra of the tensor product of B with C, called separability idempotents. The conditions include the existence of non-degenerate anti-homomorphisms from B to M(C) and from C to M(B), the multiplier algebras of C and B respectively. They are called the antipodal maps. There also exist what we call distinguished linear functionals. They are unique and faithful in the regular case. The notion is more restrictive than what is generally considered in the case …

A note on commutators in algebras of unbounded operators

We show that the identity is the sum of two commutators in the algebra of all operators affiliated with a von Neumann algebra of type II$_1$, settling a question, in the negative, that had puzzled a number of us.

单位圆盘上有界导数解析函数空间上的广义幂等元

Generalized idempotents on the space of analytic functions with bounded derivatives

研究单位圆盘上有界导数解析函数空间上广义双循环幂等元的结构，通过定义相关映射并利用其性质进行分析。

Locally bounded perturbations and (odd) unbounded KK-theory

A regular symmetric operator on a Hilbert module is self-adjoint whenever there exists a suitable approximate identity. We say an operator is 'locally bounded' if the composition of the operator with each element in the approximate identity is bounded. We prove that the perturbation of a regular self-adjoint operator by a locally bounded symmetric operator is again regular and self-adjoint. We use this result to show that the Kasparov class represented by an unbounded Kasparov module is stable under locally bounded perturbations. As an application, we show that we obtain a converse to the 'dou…

Operator algebras with contractive approximate identities: A large operator algebra in c0

We exhibit a singly generated, semisimple commutative operator algebra with a contractive approximate identity, such that the spectrum of the generator is a null sequence and zero, but the algebra is not the closed linear span of the idempotents associated with the null sequence and obtained from the analytic functional calculus. Moreover the multiplication on the algebra is neither compact nor weakly compact. Thus we construct a `large' operator algebra of orthogonal idempotents, which may be viewed as a dense subalgebra of c0.