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Higher-dimensional virtual diagonals and ideal cohomology for triangular algebras. (English) Zbl 0873.47028

Summary: We investigate the cohomology of non-self-adjoint algebras using virtual diagonals and their higher-dimensional generalizations. We show that infinite dimensional nest algebras always have non-zero second cohomology by showing that they cannot possess 2-virtual diagonals. In the case of the upper triangular atomic nest algebra we exhibit concrete modules for non-vanishing cohomology.

MSC:

47L30 Abstract operator algebras on Hilbert spaces
46H25 Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX)
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