Clifford algebras over Hilbert C*-modules

被引：0

作者：

Gao, Mingchu ^{[1
,2
]}

机构：

[1] Louisiana Coll, Div Math & Comp Sci, Pineville, LA 71359 USA

[2] Shanxi Normal Univ, Coll Math & Comp Sci, Linfen 041004, Peoples R China

来源：

HOUSTON JOURNAL OF MATHEMATICS | 2007年 / 33卷 / 04期

关键词：

Hilbert C*-modules; Clifford algebras; tensor products;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Clifford algebras of real Hilbert C*-modules with orthonormal bases are introduced. It is showed that the C*-Clifford algebra of a real Hilbert module over a real C*-algebra is *-isomorphic to the spacial tensor product of the complexification C*-algebra and a UHF C*-algebra. The von Neumann Clifford algebra of a real Hilbert module over a von Neumann algebra is *-isomorphic to the von Neumann algebra tensor product of the complexification von Neumann algebra and the hyper-finite type II1 factor.

引用

页码：1183 / 1214

页数：32

共 50 条

[31] G-FRAMES IN HILBERT MODULES OVER PRO-C*-ALGEBRAS
Hosseini, Sedigheh
Bodaghi, Abasalt
Mousavi, Lida
[J]. UNIVERSITY POLITEHNICA OF BUCHAREST SCIENTIFIC BULLETIN-SERIES A-APPLIED MATHEMATICS AND PHYSICS, 2021, 83 (04): : 35 - 44
[32] Induced representations of Hilbert modules over locally C*-algebras and the imprimitivity theorem
Karimi, Khadijeh
Sharifi, Kamran
[J]. MATHEMATICAL COMMUNICATIONS, 2016, 21 (01) : 85 - 96
[33] Some Properties of *-frames in Hilbert Modules Over Pro-C*-algebras
Irani, Mona Naroei
Nazari, Akbar
[J]. SAHAND COMMUNICATIONS IN MATHEMATICAL ANALYSIS, 2019, 16 (01): : 105 - 117
[34] Completely positive maps: pro-C∗-algebras and Hilbert modules over pro-C∗-algebras
Amin, Bhumi
Golla, Ramesh
[J]. POSITIVITY, 2024, 28 (05)
[35] Finite generation in C*-algebras and Hilbert C*-modules
Blecher, David P.
Kania, Tomasz
[J]. STUDIA MATHEMATICA, 2014, 224 (02) : 143 - 151
[36] Unbounded operators on Hilbert C*-modules and C*-algebras
Schmudgen, Konrad
[J]. DIVERSITY AND BEAUTY OF APPLIED OPERATOR THEORY, 2018, 268 : 429 - 441
[37] The Irreducibility of C*-algebras Acting on Hilbert C*-modules
Jiang, Runliang
[J]. FILOMAT, 2016, 30 (09) : 2425 - 2433
[38] Point modules over regular graded skew Clifford algebras
Vancliff, Michaela
Veerapen, Padmini P.
[J]. JOURNAL OF ALGEBRA, 2014, 420 : 54 - 64
[39] On Graded Semigroup C*-Algebras and Hilbert Modules
Lipacheva, E., V
[J]. PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS, 2021, 313 (01) : 120 - 130
[40] A triangle inequality in Hilbert modules over matrix algebras
Farenick, DR
Psarrakos, PJ
[J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 2002, 341 (1-3) : 57 - 67

← 1 2 3 4 5 →