Vektorraumbündel und der Raum der Fredholm-Operatoren

Jänich, Klaus

doi:10.1007/bf01360851

Cited by 78 publications

(43 citation statements)

References 10 publications

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“…The homomorphism a\. We shall denote by U the inductive limit Hm U(n) of unitary groups and F = BUXZ\ where BUis the classifying space of U: the space of Fredholm operators [7]. Let B denote a finite CW-complex and a£Hom(2£S0, 2£ A ) [9] …”

Section: Y') Associated To Elements Of H*(b)®h*(y Y')mentioning

confidence: 99%

Fiber cobordism and the index of a family of elliptic differential operators

Shih¹

1966

Bull. Amer. Math. Soc.

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Section: Y') Associated To Elements Of H*(b)®h*(y Y')mentioning

confidence: 99%

Fiber cobordism and the index of a family of elliptic differential operators

Shih¹

1966

Bull. Amer. Math. Soc.

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“…The key point is that the space Fred(H) of Fredholm operators on a separable Hilbert space H endowed with the norm topology, which itself has the homotopy type of Z × BU [4,12], carries a conjugation action by the group PU(H) of projective unitary operators. Thus, to a pair (X, P ) of a CW-complex X together with a principal PU(H)-bundle PU(H) → P → X over X, one can associate the twisted K-theory groups K −i (X, P ) (see [2]) defined as the homotopy groups…”

Section: The Case G = Pu(h) the Projective Unitary Groupmentioning

confidence: 99%

Equivariant principal bundles and their classifying spaces

Lück

Uribe

2014

Algebr. Geom. Topol.

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“…sect.3, p.12). It is well known (see [1] and [5] where B(H) c.o is the space of bounded operators in H, with the compact-open topology, and K(H) u is the space of compact operators in H, with the uniform topology. Let X be a compact space.…”

Section: Corollarymentioning

confidence: 99%

On Compact and Fredholm Operators over C*-algebras and a New Topology in the Space of Compact Operators

Irmatov¹,

Mishchenko

2008

J K-Theor

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It is shown that the class of Fredholm operators over an arbitrary unital C * -algebra, which may not admit adjoint ones, can be extended in such a way that this class of compact operators, used in the definition of the class of Fredholm operators, contains compact operators both with and without existence of adjoint ones. The main property of this new class is that a Fredholm operator which may not admit an adjoint one has a decomposition into a direct sum of an isomorphism and a finitely generated operator.In the space of compact operators in the Hilbert space a new IMtopology is defined. In the case when the C * -algebra is a commutative algebra of continuous functions on a compact space the IM-topology fully describe the set of compact operators over the C * -algebra without assumption of existence bounded adjoint operators over the algebra.

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Vektorraumbündel und der Raum der Fredholm-Operatoren

Cited by 78 publications

References 10 publications

Fiber cobordism and the index of a family of elliptic differential operators

Fiber cobordism and the index of a family of elliptic differential operators

Equivariant principal bundles and their classifying spaces

On Compact and Fredholm Operators over C*-algebras and a New Topology in the Space of Compact Operators

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