An index theorem for the product of linear relations

✍ Scribed by R.W. Cross

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 245 KB
• Volume: 277
• Category: Article
• ISSN: 0024-3795
• DOI: 10.1016/s0024-3795(97)10051-9

✦ Synopsis

Let X, Y and Z be vector spaces and let T and S be linear relations fromX to Y and Y to Z, respectively, with S everywhere defined on Y. A formula which relates the nullities and deficiencies of S, T and ST is derived. In the case when S and T have finite indices (in particular, when the vector spaces are all finite dimensional), then ST has an index given by index(ST) = index(S) + index(T) -dim T(0) N S ~(0).

The familiar index formula for the product of Fredholm operators is covered by the case T(0) = {0}.