论文标题
与半群相关的FOCK表示产生的有界乘数代数
Bounded multiplier algebras arising from Fock representation associated to semigroups
论文作者
论文摘要
在本文中，我们试图介绍与Fock表示相关的“乘数代数”，该表示是由左综合性半群$ \ Mathcal {s} $（由$ M（\ Mathcal {s}）$表示，通过采用$ C^*$ - alge-alge-algebra的多重层的概念，是通过$ M（\ Mathcal {s}）$。然后，我们研究了乘数代数的基本属性和示例。为了理解乘数代数，我们建立了乘数代数的两个关键结果。我们证明，如果$ \ Mathcal {s} $是左综合半群，则$ M（\ Mathcal {s}）$是Unital Banach代数。在考虑因素中，$ g $是一个组，我们证明$ m（g）$是$ c^*$ - 代数。 我们说明了关联的乘数代数$ m（\ Mathbb {z} _ {+}），M（\ Mathbb {z}^2 _+）$识别，以相应的hardy代数$ h^{\ infty}（\ mathbb {d}）$ and $ h^{ $ \ MATHCAL {s} = \ MATHBB {Z} _ {+}，\ Mathbb {Z}^2 _ {+}。我们清楚地表明，众所周知的非共同硬性代数$ \ mathbb {f} _ {n}^{\ infty} $（由G. popescu）和乘数代数$ m（\ mathbb {\ mathbb {f} _ {n} _ {n}^+）is is is is is is is is is is is is is isomem isom isom isom isom isom isom isom， 最后，使用操作员太空技术，我们已经证明了一个有趣的结果，即$ M（\ Mathcal {s}）$是操作员代数（特别是由于著名的Blecher-Ruan-Sinclair定理）。
In this article, we attempt to introduce the "Multiplier algebra" associated to the Fock representation that arising from the left-cancellative semigroup $\mathcal{S}$ (denoted by $M(\mathcal{S})$) by adopting the concept of multiplier algebra of a $C^*$-algebra. Then, we investigate the basic properties and examples of the multiplier algebras. In order to make sense of multiplier algebra, we establish two key results of the multiplier algebras. We demonstrate that $M(\mathcal{S})$ is an unital Banach algebra if $\mathcal{S}$ is a left-cancellative semigroup. In the consideration, $G$ is a group, we demonstrate that $M(G)$ is a $C^*$-algebra. We illustrate that the associated multiplier algebras $M(\mathbb{Z}_{+}), M(\mathbb{Z}^2_+)$ are identified with respective Hardy algebras $H^{\infty}(\mathbb{D})$ and $H^{\infty}(\mathbb{D}^2)$ for $\mathcal{S}=\mathbb{Z}_{+}, \mathbb{Z}^2_{+}.$ Next, we discuss that multiplier algebra associated to the free semigroup $\mathcal{S}=\mathbb{F}^+_{n}$. We clearly show that the well-known non-commutative Hardy algebra $\mathbb{F}_{n}^{\infty}$ (introduced and thoroughly studied by G. Popescu) and the multiplier algebra $M(\mathbb{F}_{n}^+)$ are isometrically isomorphic. Finally, using the operator space technique, we have demonstrated an intriguing result that $M(\mathcal{S})$ is an operator algebra (specifically, thanks to celebrated Blecher-Ruan-Sinclair theorem).
