Reducing Subspaces for a Class of Multiplication Operators

By Kehe Zhu. 2000

92 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/07e9d4846df99a12cf0f4df6fbe183269604039b

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In Applied Mathematics

Citations in the corpus

Reducing subspaces of weighted shift operators (2002, result): “A special case of our results was obtained in [7].”
Multiplication operators on the Bergman space via the Hardy space of the bidisk (2009, methodology): “As a consequence, we completely classify reducing subspaces of the multiplication operator by a Blaschke product φ with order three on the Bergman space to solve a conjecture of Zhu [40].”
Multiplication operators on the Bergman space via analytic continuation (2009, methodology): “This paper is motivated by Richter’s work on unitary equival ence of invariant subspaces of the Bergman space [21], Stephenson’s work on hyper groups [23], [24], [25] and Zhu’s conjecture on the number of minimal reducing subsp aces ofMφ [33].”
On multiplication operators on the Bergman space: Similarity, unitary equivalence and reducing subspaces (2011, background): “Zhu [25] conjectured that for a finite Blaschke product B of degree n, there are always n different minimal reducing subspaces.”
Reducing Subspace of Analytic Toeplitz Operators on the Bergman Space (2004, background): “[7], [9], [11], [14] for examples) have been made to describe the structure of the reducing subspace of Mφ (on La(D)) with φ a finite Blaschke product.”
Reducing subspaces for analytic multipliers of the Bergman space (2011, background): “Progress in understanding the lattice of reducing subspaces of Mφ was only recently made, and only in the case of inner function symbols [4, 5, 6, 7, 8, 10, 11, 14].”