对称空间上的Lp-分布

A study of symmetric points in Banach spaces

We completely characterize the left-symmetric points, the right-symmetric points, and, the symmetric points in the sense of Birkhoff-James, in a Banach space. We obtain a complete characterization of the left-symmetric (right-symmetric) points in the infinity sum of two Banach spaces, in terms of the left-symmetric (right-symmetric) points of the constituent spaces. As an application of this characterization, we explicitly identify the left-symmetric (right-symmetric) points of some well-known three-dimensional polyhedral Banach spaces.

紧对称空间上球面分布的傅里叶变换

Fourier transforms of spherical distributions on compact symmetric spaces

在我们以前的文章“A local Paley-Wiener theorem for compact symmetric spaces”，Adv. Math. 218（2008），202- 215和“傅里叶级数on compact symmetric spaces”（已提交）中，我们研究了紧致对称空间M=U/K上的傅里叶级数。特别地，我们证明了M上的光滑函数的Paley-Wiener型定理，这些光滑函数具有足够小的支撑，并且是K-不变的，分别是K-有限的。在本文中，我们将这些结果推广到M上的K不变分布。我们证明了一个分布的傅里叶变换，这是支持在一个足够小的球周围的基点，扩展到一个全纯函数的指数型。我们在全纯函数空间中描述了傅里叶变换的象。我们用分布的傅里叶变换刻画了分布的奇异支撑。最后，我们利用Paley-Wiener定理刻画了在给定不变微分算子范围内的小支撑的分布。

Banach Envelopes in Symmetric Spaces of Measurable Operators

We study Banach envelopes for commutative symmetric sequence or function spaces, and noncommutative symmetric spaces of measurable operators. We characterize the class $(HC)$ of quasi-normed symmetric sequence or function spaces $E$ for which their Banach envelopes $\widehat{E}$ are also symmetric spaces. The class of symmetric spaces satisfying $(HC)$ contains but is not limited to order continuous spaces. Let $\mathcal{M}$ be a non-atomic, semifinite von Neumann algebra with a faithful, normal, $σ$-finite trace $τ$ and $E$ be as symmetric function space on $[0,τ(1))$ or symmetric sequence sp…

Duality for symmetric Hardy spaces of noncommutative martingales

We show the dual spaces of conditional Hardy space and symmetric Hardy space of noncommutative martingales. We derive relationship between the symmetric Hardy space of noncommutative martingales and its conditioned version.

简单生成对称空间上的对称泛函

Symmetric functionals on simply generated symmetric spaces

本文提出在半有限冯·诺依曼代数的对称空间上构造对称泛函的方法，建立了其与有界序列平移不变泛函间的双射，并据此扩展了 Connes 迹公式。

紧对称空间的全纯索伯列夫空间

Holomorphic Sobolev spaces associated to compact symmetric spaces

利用Gutzmer的公式，由于Lassalle，我们证明了索伯列夫空间在Segal-Bargmann变换下在紧致黎曼对称空间上的象.