Extreme points of the unit ball of an operator space

The unit ball of an injective operator space has an extreme point

We define an $AW^*$-TRO as an off-diagonal corner of an $AW^*$-algebra, and show that the unit ball of an $AW^*$-TRO has an extreme point. In particular, the unit ball of an injective operator space has an extreme point, which answers a question raised in the author's previous work [Journal of Operator Theory, 76(2) (2016), 219-248] affirmatively. We also show that an $AW^*$-TRO (respectively, an injective operator space) has an ideal decomposition, that is, it can be decomposed into the direct sum of a left ideal, a right ideal, and a two-sided ideal in an $AW^*$-algebra (respectively, an inj…

单位球Bergman空间上Toeplitz代数中Toeplitz算子的密度研究

On the density of Toeplitz operators in the Toeplitz algebra over the Bergman space of the unit ball

该研究采用量子调和分析与表示论方法，给出单位球Bergman空间上Toeplitz代数中Toeplitz算子按范数稠密的夏氏定理的新证明。

Free holomorphic functions on the unit ball of B(H)^n. II

In this paper we continue the study of free holomorphic functions on the unit ball of B(H)^n, where B(H) is the algebra of all bounded linear operators on a Hilbert space H. Several classical results from complex analysis have free analogues in our noncommutative setting.

C*-Convexity of Norm Unit Balls

We determine those norms on B(H) whose unit ball is C*-convex. We call them M-norms and show that the class of M-norms less than a given norm enjoys a maximum element. These minimum and maximum elements will be determined in some cases. Finally, we give a constructive result to obtain M-norms on B(H).

Characteristic functions for multicontractions and automorphisms of the unit ball

A \emph{multicontraction} on a Hilbert space $\HH$ is an $n$-tuple of operators $T=(T_1,...,T_n)$ acting on $\HH$, such that $\sum_{i=1}^n T_i T_i^*\le \1_\HH$. We obtain some results related to the characteristic function of a commuting multicontraction, most notably discussing its behaviour with respect to the action of the analytic automorphisms of the unit ball.

Unitarizable representations and fixed points of groups of biholomorphic transformations of operator balls

We show that the open unit ball of the space of operators from a finite dimensional Hilbert space into a separable Hilbert space (we call it "operator ball") has a restricted form of normal structure if we endow it with a hyperbolic metric (which is an analogue of the standard hyperbolic metric on the unit disc in the complex plane). We use this result to get a fixed point theorem for groups of biholomorphic automorphisms of the operator ball. The fixed point theorem is used to show that a bounded representation in a separable Hilbert space which has an invariant indefinite quadratic form with…