A trace formula for isometric pairs

Rongwei Yang

doi:10.1090/S0002-9939-02-06687-X

A trace formula for isometric pairs

Rongwei Yang

Mathematics and Statistics

University at Albany

Research output: Contribution to journal › Article › peer-review

10 Scopus citations

Abstract

It is well known that for every isometry V, tr[V*, V] = -ind(V). This fact for the shift operator is a basis for many important developments in operator theory and topology. In this paper we prove an analogous formula for a pair of isometries (V₁, V₂), namely tr[V₁*, V₁,V₂*,V₂] = -2ind(V₁,V₂), where [V₁*, V₁, V₂*, V₂] is the complete anti-symmetric sum and ind(V₁, V₂) is the Fredholm index of the pair (V₁, V₂). The major tool is what we call the fringe operator. Two examples are considered.

Original language	English
Pages (from-to)	533-541
Number of pages	9
Journal	Proceedings of the American Mathematical Society
Volume	131
Issue number	2
DOIs	https://doi.org/10.1090/S0002-9939-02-06687-X
State	Published - Feb 2003

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AB - It is well known that for every isometry V, tr[V*, V] = -ind(V). This fact for the shift operator is a basis for many important developments in operator theory and topology. In this paper we prove an analogous formula for a pair of isometries (V1, V2), namely tr[V1*, V1,V2*,V2] = -2ind(V1,V2), where [V1*, V1, V2*, V2] is the complete anti-symmetric sum and ind(V1, V2) is the Fredholm index of the pair (V1, V2). The major tool is what we call the fringe operator. Two examples are considered.

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JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

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A trace formula for isometric pairs

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