Closed and sigma-finite measures on the orthogonal projections

关于正交投影与上半平面多项式Bergman空间上Toeplitz算子关系的研究：垂直符号

On a relationship between orthogonal projections and Toeplitz operators on poly-Bergman spaces of the upper half-plane: vertical symbols

本文研究了上半平面多项式Bergman空间上正交投影与Toeplitz算子的关系，引入了几乎全部正交投影，并展示了由此生成的C*-代数与具有边界条件的垂直符号Toeplitz算子生成的C*-代数之间的紧密联系。

$C^*$-algebras generated by three projections

In this short note, we prove that for a $C^*$-algebra $å$ generated by $n$ elements, $M_{k}(\tildeå)$ is generated by $k$ mutually unitarily equivalent and almost mutually orthogonal projections for any $k\ge \de(n)=\min\big\{k\in\mathbb N\,|\,(k-1)(k-2)\ge 2n\big\}$. Then combining this result with recent works of Nagisa, Thiel and Winter on the generators of $C^*$--algebras, we show that for a $C^*$-algebra $å$ generated by finite number of elements, there is $d\ge 3$ such that $M_d(\tilde A)$ is generated by three mutually unitarily equivalent and almost mutually orthogonal projections. Fur…

Extension of projection mappings

We show that a map between projection lattices of semi-finite von Neumann algebras can be extended to a Jordan $*$-homomorphism between the von Neumann algebras if this map is defined in terms of the support projections of images (under the linear map) of projections and the images of orthogonal projections have orthogonal support projections. This has numerous fundamental applications in the study of isometries and composition operators on quantum symmetric spaces and is of independent interest, since it provides a partial generalization of Dye's Theorem without the requirement that the initi…

两个正交投影的乘积

Products of two orthogonal projections

研究两个正交投影的乘积算子，补充Crimmins和von Neumann的经典结果，特别关注多圆盘上内函数相关的投影。

On Fourier orthogonal projections in the rotation algebra

Projections are constructed in the rotation algebra that are orthogonal to their Fourier transform and which are fixed under the flip automorphism. Such projections are expected in a construction of an inductive limit structure for the irrational rotation algebra that is invariant under the Fourier transform. (Namely, as two circle algebras of the same dimension, that are swapped by the Fourier transform, plus a few points.) The calculation is based on Rieffel's construction of the Schwartz space as an equivalence bimodule of rotation algebras as well as on the theory of Theta functions.

Yang-Mills connections and sigma-models on quantum Heisenberg manifolds

We construct a spectral triple on a quantum Heisenberg manifold, which generalizes the results of Chakraborty and Shinha, and associate to it an energy functional on the set of projections, following the approach of Mathai-Rosenberg to non-linear sigma models. The spectral triples that we construct extend the We derive a lower bound for this energy functional that is linked on the topological charge of the projection which depends on the curvature of a compatible connection. A detailed study of this lower bound is given for the Kang projection in quantum Heisenberg manifolds. These results dis…