C*-algebra of nonlocal convolution type operators

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:475

Article

Karlovich, Yuri I.¹  Loreto-Hernandez, Ivan² 

[1] Univ Autonoma Estado Morelos, Ctr Invest Ciencias, Inst Invest Ciencias Basicas & Aplicadas, Ave Univ 1001, Cuernavaca 62209, Morelos, Mexico

[2] Univ Juarez Autonoma Tabasco, Consejo Nacl Ciencia & Tecnol, Div Acad Ciencias Basicas, Carretera Cunduacan Jalpa Mendez Km 1, Cunduacan 86690, Tabasco, Mexico

关键词: C*-algebra of convolution type operators with shifts;    Piecewise slowly oscillating function;    Local-trajectory method;    Spectral measure;    Faithful representation;    Fredholmness;   

DOI  :  10.1016/j.jmaa.2018.11.085

来源: Elsevier

【 摘 要 】

The C*-subalgebra B of all bounded linear operators on the space L-2 (R), which is generated by all multiplication operators by piecewise slowly oscillating functions, by all convolution operators with piecewise slowly oscillating symbols and by the range of a unitary representation of the group of all affine mappings on R, is studied. A faithful representation of the quotient C*-algebra B-pi = B/K in a Hilbert space, where k is the ideal of compact operators on the space L-2 (R), is constructed by applying an appropriate spectral measure decompositions, a local-trajectory method and the Fredholm symbol calculus for the C*-algebra of convolution type operators without shifts. This gives a Fredholm symbol calculus for the C*-algebra 93 and a Fredholm criterion for the operators B is an element of 93. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

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