## Relative K-homology and normal operators

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### Standard

Relative K-homology and normal operators. / Manuilov, Vladimir; Thomsen, Klaus.

I: Journal of Operator Theory, Bind 62, Nr. 2, 2009, s. 249-279.

Publikation: Bidrag til tidsskrift/Konferencebidrag i tidsskrift /Bidrag til avisTidsskriftartikelForskningpeer review

### Harvard

Manuilov, V & Thomsen, K 2009, 'Relative K-homology and normal operators', Journal of Operator Theory, bind 62, nr. 2, s. 249-279.

### APA

Manuilov, V., & Thomsen, K. (2009). Relative K-homology and normal operators. Journal of Operator Theory, 62(2), 249-279.

### CBE

Manuilov V, Thomsen K. 2009. Relative K-homology and normal operators. Journal of Operator Theory. 62(2):249-279.

### MLA

Manuilov, Vladimir og Klaus Thomsen. "Relative K-homology and normal operators". Journal of Operator Theory. 2009, 62(2). 249-279.

### Vancouver

Manuilov V, Thomsen K. Relative K-homology and normal operators. Journal of Operator Theory. 2009;62(2):249-279.

### Author

Manuilov, Vladimir ; Thomsen, Klaus. / Relative K-homology and normal operators. I: Journal of Operator Theory. 2009 ; Bind 62, Nr. 2. s. 249-279.

### Bibtex

@article{b8298ee0b8bb11de82fe000ea68e967b,
title = "Relative K-homology and normal operators",
abstract = "Let $A$ be a $C^*$-algebra, $J \subset A$ a $C^*$-subalgebra, and let $B$ be a stable $C^*$-algebra. Under modest assumptions we organize invertible $C^*$-extensions of $A$ by $B$ that are trivial when restricted onto $J$ to become a group $\mathrm{Ext}_J^{-1}(A,B)$, which can be computed by a six-term exact sequence which generalizes the excision six-term exact sequence in the first variable of KK-theory. Subsequently we investigate the relative K-homology which arises from the group of relative extensions by specializing to abelian $C^*$-algebras. It turns out that this relative K-homology carries substantial information also in the operator theoretic setting from which the BDF theory was developed and we conclude the paper by extracting some of this information on approximation of normal operators.",
author = "Vladimir Manuilov and Klaus Thomsen",
year = "2009",
language = "English",
volume = "62",
pages = "249--279",
journal = "Journal of Operator Theory",
issn = "0379-4024",
publisher = "Academia Romana Institutul de Matematica",
number = "2",

}

### RIS

TY - JOUR

T1 - Relative K-homology and normal operators

AU - Thomsen, Klaus

PY - 2009

Y1 - 2009

N2 - Let $A$ be a $C^*$-algebra, $J \subset A$ a $C^*$-subalgebra, and let $B$ be a stable $C^*$-algebra. Under modest assumptions we organize invertible $C^*$-extensions of $A$ by $B$ that are trivial when restricted onto $J$ to become a group $\mathrm{Ext}_J^{-1}(A,B)$, which can be computed by a six-term exact sequence which generalizes the excision six-term exact sequence in the first variable of KK-theory. Subsequently we investigate the relative K-homology which arises from the group of relative extensions by specializing to abelian $C^*$-algebras. It turns out that this relative K-homology carries substantial information also in the operator theoretic setting from which the BDF theory was developed and we conclude the paper by extracting some of this information on approximation of normal operators.

AB - Let $A$ be a $C^*$-algebra, $J \subset A$ a $C^*$-subalgebra, and let $B$ be a stable $C^*$-algebra. Under modest assumptions we organize invertible $C^*$-extensions of $A$ by $B$ that are trivial when restricted onto $J$ to become a group $\mathrm{Ext}_J^{-1}(A,B)$, which can be computed by a six-term exact sequence which generalizes the excision six-term exact sequence in the first variable of KK-theory. Subsequently we investigate the relative K-homology which arises from the group of relative extensions by specializing to abelian $C^*$-algebras. It turns out that this relative K-homology carries substantial information also in the operator theoretic setting from which the BDF theory was developed and we conclude the paper by extracting some of this information on approximation of normal operators.

M3 - Journal article

VL - 62

SP - 249

EP - 279

JO - Journal of Operator Theory

JF - Journal of Operator Theory

SN - 0379-4024

IS - 2

ER -