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Journal of the London Mathematical Society 1997 55(3):499-514; doi:10.1112/S0024610796004073
© 1997 by London Mathematical Society
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© The London Mathematical Society

The Cohomology Comparison Problem for Banach Algebras

Michel Solovej

Treasury Department, Unibank AS DK-1786 V, Denmark. E-mail: riskman{at}centrum.dk

Received 23 August 1993. Revision received 18 November 1994.

For a large class of Banach algebras we solve the Cohomology Comparison Problem for the second cohomology groups, in that we prove that for all amenable strongly regular Banach function algebras A and all Banach A-bimodules E the second comparison map between continuous and algebraic cohomology is an embedding. Accepting the continuum hypothesis we show that for algebras of this kind there exist Banach A-bimodules E such that i2 is not onto.


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