Multiplication operators defined by covering maps on the Bergman space: the connection between operator theory and von Neumann algebras

DOI10.1016/j.jfa.2010.11.002zbMath1216.46054OpenAlexW2022396954MaRDI QIDQ629707

Kunyu Guo, Hansong Huang

Publication date: 9 March 2011

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jfa.2010.11.002

zbMATH Keywords

von Neumann algebrafundamental grouptype II factorholomorphic covering map

Mathematics Subject Classification ID

General theory of von Neumann algebras (46L10) Invariant subspaces of linear operators (47A15) Conformal mappings of special domains (30C20) Riemann surfaces (30F99) Bergman spaces and Fock spaces (30H20) Classification of factors (46L36)

Related Items (16)

Reducing subspaces of tensor products of weighted shifts ⋮ An Introduction to Hilbert Module Approach to Multivariable Operator Theory ⋮ Multiplication by a finite Blaschke product on weighted Bergman spaces: commutant and reducing subspaces ⋮ Geometric constructions of thin Blaschke products and reducing subspace problem ⋮ Von Neumann algebras generated by multiplication operators on the weighted Bergman space: a function-theory view into operator theory ⋮ Multiplication operators defined by twisted proper holomorphic maps on Bergman spaces ⋮ Reducing subspaces of multiplication operators with the symbol \(\alpha z^k+\beta w^l\) on \(L_a^2 (\mathbb D^2)\) ⋮ Reducing subspaces for rank-one perturbations of normal operators ⋮ On the double commutant of Cowen-Douglas operators ⋮ Reducing subspaces for analytic multipliers of the Bergman space ⋮ Multiplication operators defined by a class of polynomials on \({L_a^2(\mathbb{D}^2)}\) ⋮ Joint reducing subspaces of multiplication operators and weight of multi-variable Bergman spaces ⋮ Multiplication operators on the Bergman spaces of polygons ⋮ Reducing subspaces of multiplication operators on function spaces ⋮ Reducing subspaces for the product of a forward and a backward operator-weighted shifts ⋮ Reducing subspaces of some multiplication operators on the Bergman space over polydisk

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