2005年11月17日 · We also show that $C^*(G)$ is GCR if and only if $\go/G$ is a $T_0$ topological space and all of the isotropy groups are GCR. Subjects: Operator Algebras (math.OA)

2019年1月18日 · In this paper we characterize when the algebra of an ample groupoid over a field is CCR and GCR. The results turn out to be exact analogues of the corresponding characterization of locally compact groupoids with CCR and GCR $C^*$-algebras. As a consequence, we classify the CCR and GCR Leavitt path algebras.

arXiv:1901.06056v2 [math.OA] 10 Aug 2019 GCR AND CCR STEINBERG ALGEBRAS LISA ORLOFF CLARK, BENJAMIN STEINBERG, AND DANIEL W VAN WYK Abstract. Kaplansky introduced the notions of CCR and GCR C∗-algebras because they have a tractable representation theory. Many years later, he introduced the notions of CCR and GCR rings. In this

A GCR algebra is a C*-algebra $A$ such that $\mathrm{CCR}(A/J)\neq 0$ for all ideals $J\neq A$. Basically this means that the irreducible representations of C*-algebras contain all compact operators. In particular, finite dimensional C*-algebras …

2016年2月10日 · Let A A be a simple GCR C*-algebra and π: A → B(H) π: A → B (H) be an irreducible C*-algebra. Since A A is simple then π π is one to one and so it is an isometry. Since A A is GCR then K(H) ⊆ π(A) K (H) ⊆ π (A).

In this paper we characterize when the algebra of an ample groupoid over a field is CCR and GCR. The results turn out to be exact analogues of the corresponding characterization of locally compact groupoids with CCR and GCR $C^ {\ast }$ -algebras. As a consequence, we classify the CCR and GCR Leavitt path algebras.

2018年3月25日 · Understanding the Generalized Conjugate Residual (GCR) method. I'm given the following description of the GCR algorithm: I think I understand all the steps until: β = (vi,ri−1) ui:= ui−1 + βsi β = (v i, r i − 1) u i:= u i − 1 + β s i. Question: What does βsi β s i look like? Should I compute βsi = visi1 +ri−1si2 β s i = v i s 1 i + r i − 1 s 2 i?

设𝒜为C*代数，如果对𝒜的每个 不可约表示 (H,π)，都有π (𝒜)⊂𝒦 (H)（即H上紧算子全体），则称𝒜是CCR代数。 CCR代数是具有紧表示的C*代数，每个有限维C*代数都是CCR代数。 设𝒜为C*代 …

2019年6月21日 · In this paper, we introduce constant slope (CS) and generalized constant ratio (GCR) submanifolds with higher codimension in Euclidean spaces. We firstly obtain a classification of GCR surfaces in Euclidean 4-spaces \ ( {\mathbb {E}}^4\). Then, we get complete local classification of CS surfaces in \ ( {\mathbb {E}}^4\).

The groupoid C ∗-algebra C (G) is GCR if and only if the orbit space is T0 and the isotropy groups are GCR. Date: October 16, 2018. 1991 Mathematics Subject Classification. 46L05,46L35. Key words and phrases. Locally Compact groupoid, C∗-algebra, Hilbert Module. 1