An algebraic version of the multiplication property of the Fredholm index
type: Item
instance of: scholarly article
title: An algebraic version of the multiplication property of the Fredholm index
zbMATH Open document ID: 0822.47013
DOI: 10.1016/0024-3795(94)90440-5
published in: Linear Algebra and its Applications
publication date: 1995-10-22T00:00:00Z
review text: Let \(X\), \(Y\), \(Z\) be vector spaces and \(T: X\to Y\), \(S: Y\to Z\) everywhere defined linear operators. It is shown that \[ \dim\ker ST+ \text{codim ran } S+ \text{codim ran } T= \text{codim ran } ST+ \dim\ker S+ \dim\ker T. \] The well-known index formula \(\text{ind } ST= \text{ind } T+\text{ind } S\) is thus seen to hold not only when the quantities involved are all finite, but also whenever the cardinal arithmetic makes sense (for example, when \(S\) and \(T\) both have finite-dimensional kernels).
reviewed by: R. W. Cross
Mathematics Subject Classification ID: 47A53
Mathematics Subject Classification ID: 15A04
zbMATH DE Number: 665786
zbMATH Keywords: Fredholm operator
author: Don Hadwin
MaRDI profile type: Publication
full work available at URL: 0024-3795(94)90440-5
OpenAlex ID: W2076508327
cites work: Q5803586
cites work: The Multiplication Theorem for Fredholm Operators
description: scientific article; zbMATH DE number 665786