nLab Israel Gelfand

Israel Moiseevich Gel’fand (Израиль Гельфанд, 1913–2009) played a preeminent role in Russian mathematics for many years. His legendary seminar in Moscow ran for 50 years, and set the pattern for many others, including Sullivan’s seminar at CUNY and Drinfeld’s at Chicago. His name is attached to many mathematical achievements, including

• the Gelfand representation? of a Banach algebra,

• an important special case, the Gelfand-Naimark theorem describing commutative C*-algebras,

• the Gelfand-Naimark-Segal construction describing general C-algebras,

• the Gelfand-Fuks cohomology of a foliation,

• the Gelfand-Kirillov dimension? of an associative algebra,

• the Bernstein-Gelfand-Gelfand resolution for representations of simple Lie groups.

• Gel'fand triple

He helped write a 5-volume work on distribution theory.

Selected writings

Introducing the GNS construction:

• Israel Gelfand, Mark Naimark, On the imbedding of normed rings into the ring of operators on a Hilbert space, Matematicheskii Sbornik. 12 (2): 197–217 (1943)

  reprinted in:

  Robert Doran (ed.), $C^\ast$-Algebras: 1943–1993, Contemporary Mathematics 167, AMS 1994 (doi:10.1090/conm/167)

category: people