### Abstract

Let A be a separable nuclear C^{+} algebra with unit. Let g{script} be a closed two-sided ideal in A. A relative K homology group K^{0}(A,g{script}) is defined. Closely related are topological definitions of properly supported K homology and of compactly supported relative K homology. Applications are to indices of Toeplitz operators and existence of coercive boundary conditions for elliptic differential operators.

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

Pages (from-to) | 1-46 |

Number of pages | 46 |

Journal | K-Theory |

Volume | 5 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1 1991 |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)

### Cite this

^{*}algebras.

*K-Theory*,

*5*(1), 1-46. https://doi.org/10.1007/BF00538877

}

^{*}algebras',

*K-Theory*, vol. 5, no. 1, pp. 1-46. https://doi.org/10.1007/BF00538877

**Relative K homology and C ^{*} algebras.** / Baum, Paul Frank; Douglas, Ronald G.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Relative K homology and C* algebras

AU - Baum, Paul Frank

AU - Douglas, Ronald G.

PY - 1991/1/1

Y1 - 1991/1/1

N2 - Let A be a separable nuclear C+ algebra with unit. Let g{script} be a closed two-sided ideal in A. A relative K homology group K0(A,g{script}) is defined. Closely related are topological definitions of properly supported K homology and of compactly supported relative K homology. Applications are to indices of Toeplitz operators and existence of coercive boundary conditions for elliptic differential operators.

AB - Let A be a separable nuclear C+ algebra with unit. Let g{script} be a closed two-sided ideal in A. A relative K homology group K0(A,g{script}) is defined. Closely related are topological definitions of properly supported K homology and of compactly supported relative K homology. Applications are to indices of Toeplitz operators and existence of coercive boundary conditions for elliptic differential operators.

UR - http://www.scopus.com/inward/record.url?scp=0039164608&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0039164608&partnerID=8YFLogxK

U2 - 10.1007/BF00538877

DO - 10.1007/BF00538877

M3 - Article

AN - SCOPUS:0039164608

VL - 5

SP - 1

EP - 46

JO - K-Theory

JF - K-Theory

SN - 0920-2036

IS - 1

ER -

^{*}algebras. K-Theory. 1991 Jan 1;5(1):1-46. https://doi.org/10.1007/BF00538877