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The Cohomology Comparison Problem for Banach Algebras
Author(s) -
Solovej Michel
Publication year - 1997
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610796004073
Subject(s) - cohomology , mathematics , embedding , pure mathematics , banach manifold , banach algebra , class (philosophy) , group cohomology , eberlein–šmulian theorem , algebra over a field , banach space , lp space , computer science , artificial intelligence
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 i 2 is not onto.