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Abstract $$\overline {\partial}$$-resolutions for several commuting operators. (English) Zbl 0842.47004
Curto, Raúl E. (ed.) et al., Multivariable operator theory. A joint summer research conference on multivariable operator theory, July 10-18, 1993, University of Washington, Seattle, WA, USA. Providence, RI: American Mathematical Society. Contemp. Math. 185, 319-337 (1995).
Summary: We relate several spectral decomposition and spectral localization properties of commuting systems of Banach space operators to some distinguished resolutions of the corresponding analytic modules. A universal dilation for commuting tuples of operators and the relationship between spectral sets and generalized scalar dilations are also included in this framework. A few applications to function theory and complex geometry are derived from the main abstract results.
For the entire collection see [Zbl 0819.00022].
##### MSC:
 47A11 Local spectral properties of linear operators 46M20 Methods of algebraic topology in functional analysis (cohomology, sheaf and bundle theory, etc.) 32C35 Analytic sheaves and cohomology groups