منابع مشابه
Surgery and the Relative Index in Elliptic Theory
This is a survey article intended as an elementary introduction to the general index locality principle introduced in [17]. We discuss it and give some examples of its consequences and applications showing that this principle often proves to be a powerful tool for obtaining index formulas in various situations. Having in mind the introductory character of the article, we try to keep the exposit...
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Lecture Notes taken by Nilufer Koldan In this lecture I will describe one of the most significant achievements of the second half of the XX century – the Atiyah-Singer index theorem. I will also discuss some more recent developments in the area as well as some open problems. 1. The definition of the index 1.1. The finite-dimensional case. Let A : V 1 → V 2 be a linear map between finite dimensi...
متن کاملRanks of modules relative to a torsion theory
Relative to a hereditary torsion theory $tau$ we introduce a dimension for a module $M$, called {em $tau$-rank of} $M$, which coincides with the reduced rank of $M$ whenever $tau$ is the Goldie torsion theory. It is shown that the $tau$-rank of $M$ is measured by the length of certain decompositions of the $tau$-injective hull of $M$. Moreover, some relations between the $tau$-rank of $M$ and c...
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The double angle theorems of Davis and Kahan bound the change in an invariant subspace when a Hermitian matrix A is subject to an additive perturbation A ! e A = A+A. This paper supplies analogous results when A is subject to a congruential, or multiplicative, perturbation A ! e A = D AD. The relative gaps that appear in the bounds involve the spectrum of only one matrix, either A or e A, in co...
متن کاملRelative-sameness counterpart Theory
Just as set theory can be divorced from Ernst Zermelo’s original axiomatization of it, counterpart theory can be divorced from the eight postulates that were originally stipulated by David Lewis (1968, p. 114) to constitute it. These were postulates governing some of the properties and relations holding among possible worlds and their inhabitants. In particular, counterpart theory can be divorc...
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ژورنال
عنوان ژورنال: Journal of Functional Analysis
سال: 1992
ISSN: 0022-1236
DOI: 10.1016/0022-1236(92)90072-q