An index formula for the product of linear relations

Adrian Sandovici; Henk de Snoo

doi:10.1016/j.laa.2009.07.011

An index formula for the product of linear relations

Adrian Sandovici, Henk de Snoo^*

^*Corresponding author for this work

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

57 Citations (Scopus)

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Abstract

Let X, Y, and 3 be linear spaces and let A and B be linear relations from X to Y and from Y to 3, respectively. The main result of this note is a formula which relates the nullities and the defects of the relations A and B with those of the product relation BA. (C) 2009 Elsevier Inc. All rights reserved.

Original language	English
Pages (from-to)	2160-2171
Number of pages	12
Journal	Linear Algebra and Its Applications
Volume	431
Issue number	11
DOIs	https://doi.org/10.1016/j.laa.2009.07.011
Publication status	Published - 1-Nov-2009

Keywords

Linear space
Linear relation
Fredholm index
OPERATORS
DESCENT
THEOREM
NULLITY
DEFECT
ASCENT

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abstract = "Let X, Y, and 3 be linear spaces and let A and B be linear relations from X to Y and from Y to 3, respectively. The main result of this note is a formula which relates the nullities and the defects of the relations A and B with those of the product relation BA. (C) 2009 Elsevier Inc. All rights reserved.",

keywords = "Linear space, Linear relation, Fredholm index, OPERATORS, DESCENT, THEOREM, NULLITY, DEFECT, ASCENT",

author = "Adrian Sandovici and \{de Snoo\}, Henk",

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AU - de Snoo, Henk

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PY - 2009/11/1

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N2 - Let X, Y, and 3 be linear spaces and let A and B be linear relations from X to Y and from Y to 3, respectively. The main result of this note is a formula which relates the nullities and the defects of the relations A and B with those of the product relation BA. (C) 2009 Elsevier Inc. All rights reserved.

AB - Let X, Y, and 3 be linear spaces and let A and B be linear relations from X to Y and from Y to 3, respectively. The main result of this note is a formula which relates the nullities and the defects of the relations A and B with those of the product relation BA. (C) 2009 Elsevier Inc. All rights reserved.

KW - Linear space

KW - Linear relation

KW - Fredholm index

KW - OPERATORS

KW - DESCENT

KW - THEOREM

KW - NULLITY

KW - DEFECT

KW - ASCENT

U2 - 10.1016/j.laa.2009.07.011

DO - 10.1016/j.laa.2009.07.011

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VL - 431

SP - 2160

EP - 2171

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

IS - 11

ER -

An index formula for the product of linear relations

Abstract

Keywords

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