C*-Algebras of Meta-Invariant Operators in Modules Over Cayley-Dickson Algebras

被引：0
|
作者：
Ludkovsky, Sergey V. [1 ,2 ]
机构：
[1] Moscow State Tech Univ, MIREA, Dept Appl Math, Av Vernadsky 78, Moscow 119454, Russia
[2] Univ Bretagne Sud, Lab Math Bretagne Atlantique, UMR CNRS 6205, LMBA, F-56017 Vannes, France
来源：
SOUTHEAST ASIAN BULLETIN OF MATHEMATICS | 2015年 / 39卷 / 05期
关键词：
Hypercomplex numbers; Cayley-Dickson algebras; Operator; Operator algebra; C*-algebra; Spectra; Spectral measure;
D O I：
暂无
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Algebras of meta-invariant operators in Hilbert modules over Cayley-Dickson algebras generalizing complex C*-algebras are studied. Their structural and spectral theory are investigated. For algebras of meta-invariant operators which are analogous to Gelfand-Naimark-Segal's, von Neuman's, Kaplansky's, etc. are considered. Some related theorems are proved.
引用
收藏
页码：625 / 684
页数：60
相关论文
共 50 条
  • [21] DERIVATIONS AND CAYLEY DERIVATIONS OF GENERALIZED CAYLEY-DICKSON ALGEBRAS
    MCCRIMMON, K
    PACIFIC JOURNAL OF MATHEMATICS, 1985, 117 (01) : 163 - 182
  • [22] Roots and critical points of polynomials over Cayley-Dickson algebras
    Chapman, Adam
    Guterman, Alexander
    Vishkautsan, Solomon
    Zhilina, Svetlana
    COMMUNICATIONS IN ALGEBRA, 2023, 51 (04) : 1355 - 1369
  • [23] A CAYLEY-DICKSON PROCESS FOR A CLASS OF STRUCTURABLE ALGEBRAS
    ALLISON, BN
    FAULKNER, JR
    TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1984, 283 (01) : 185 - 210
  • [24] From Cayley-Dickson Algebras to Combinatorial Grassmannians
    Saniga, Metod
    Holweck, Frederic
    Pracna, Petr
    MATHEMATICS, 2015, 3 (04): : 1192 - 1221
  • [25] Ternary derivations of generalized Cayley-Dickson algebras
    Jiménez-Gestal, C
    Pérez-Izquierdo, JM
    COMMUNICATIONS IN ALGEBRA, 2003, 31 (10) : 5071 - 5094
  • [26] Holomorphic Functions in Generalized Cayley-Dickson Algebras
    Flaut, Cristina
    Shpakivskyi, Vitalii
    ADVANCES IN APPLIED CLIFFORD ALGEBRAS, 2015, 25 (01) : 95 - 112
  • [27] Holomorphic Functions in Generalized Cayley-Dickson Algebras
    Cristina Flaut
    Vitalii Shpakivskyi
    Advances in Applied Clifford Algebras, 2015, 25 : 95 - 112
  • [28] Quasi-associativity and Cayley-Dickson algebras
    Morita, K.
    PROGRESS OF THEORETICAL AND EXPERIMENTAL PHYSICS, 2014, 2014 (01):
  • [29] LARGE ANNIHILATORS IN CAYLEY-DICKSON ALGEBRAS II
    Biss, Daniel K.
    Christensen, J. Daniel
    Dugger, Daniel
    Isaksen, Daniel C.
    BOLETIN DE LA SOCIEDAD MATEMATICA MEXICANA, 2007, 13 (02): : 269 - 292
  • [30] Hadamard transforms and analysis on Cayley-Dickson algebras
    Ren, Guangbin
    Zhao, Xin
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2024, 537 (01)
12345