### Abstract

We establish a Fredholm criterion for the operators belonging to the C*-algebra generated by singular integral operators with semi-almost periodic matrix coefficients. The result is applied to Toeplitz-like operators that are perturbed by integral operators with fixed singularities at infinity, in which case it leads to an effectively verifiable Fredholm criterion together with an index formula. Our approach is based on an isomorphism theorem for C*-algebras associated with C*-dynamical systems and the notion of canonical generalized AP factorization for almost periodic matrix functions.

Original language | English (US) |
---|---|

Pages (from-to) | 445-484 |

Number of pages | 40 |

Journal | Journal of Functional Analysis |

Volume | 204 |

Issue number | 2 |

DOIs | |

State | Published - Nov 10 2003 |

### Fingerprint

### Keywords

- Almost periodic function
- C*-algebra
- C*-dynamical system
- Matrix function
- Semi-almost periodic function
- Singular integral operator
- Toeplitz operator

### ASJC Scopus subject areas

- Analysis

### Cite this

*Journal of Functional Analysis*,

*204*(2), 445-484. https://doi.org/10.1016/S0022-1236(03)00126-5

**The C*-algebra of singular integral operators with semi-almost periodic coefficients.** / Böttcher, A.; Karlovich, Yu I.; Spitkovsky, Ilya.

Research output: Contribution to journal › Article

*Journal of Functional Analysis*, vol. 204, no. 2, pp. 445-484. https://doi.org/10.1016/S0022-1236(03)00126-5

}

TY - JOUR

T1 - The C*-algebra of singular integral operators with semi-almost periodic coefficients

AU - Böttcher, A.

AU - Karlovich, Yu I.

AU - Spitkovsky, Ilya

PY - 2003/11/10

Y1 - 2003/11/10

N2 - We establish a Fredholm criterion for the operators belonging to the C*-algebra generated by singular integral operators with semi-almost periodic matrix coefficients. The result is applied to Toeplitz-like operators that are perturbed by integral operators with fixed singularities at infinity, in which case it leads to an effectively verifiable Fredholm criterion together with an index formula. Our approach is based on an isomorphism theorem for C*-algebras associated with C*-dynamical systems and the notion of canonical generalized AP factorization for almost periodic matrix functions.

AB - We establish a Fredholm criterion for the operators belonging to the C*-algebra generated by singular integral operators with semi-almost periodic matrix coefficients. The result is applied to Toeplitz-like operators that are perturbed by integral operators with fixed singularities at infinity, in which case it leads to an effectively verifiable Fredholm criterion together with an index formula. Our approach is based on an isomorphism theorem for C*-algebras associated with C*-dynamical systems and the notion of canonical generalized AP factorization for almost periodic matrix functions.

KW - Almost periodic function

KW - C-algebra

KW - C-dynamical system

KW - Matrix function

KW - Semi-almost periodic function

KW - Singular integral operator

KW - Toeplitz operator

UR - http://www.scopus.com/inward/record.url?scp=10744227013&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=10744227013&partnerID=8YFLogxK

U2 - 10.1016/S0022-1236(03)00126-5

DO - 10.1016/S0022-1236(03)00126-5

M3 - Article

VL - 204

SP - 445

EP - 484

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

SN - 0022-1236

IS - 2

ER -