Rank-one cross commutators on backward shift invariant subspaces on the bidisk

2009 ◽  
Vol 25 (5) ◽  
pp. 693-714 ◽  
Author(s):  
Kei Ji Izuchi ◽  
Kou Hei Izuchi
Keyword(s):  
Invariant Subspaces ◽  
Rank One ◽  
Backward Shift

scholarly journals SPECTRAL RADIUS ALGEBRAS AND C0 CONTRACTIONS. II

2010 ◽  
Vol 89 (1) ◽  
pp. 91-104 ◽  
Author(s):  
SRDJAN PETROVIC
Keyword(s):  
Spectral Radius ◽  
Invariant Subspaces ◽  
Rank One

AbstractWe consider spectral radius algebras associated with C0 contractions. When the operator A is algebraic, we describe all invariant subspaces that are common for operators in its spectral radius algebra ℬA. When the operator A is not algebraic, ℬA is weakly dense and we characterize a set of rank-one operators in ℬA that is weakly dense in ℒ(ℋ).

Ranks of backward shift invariant subspaces of the Hardy space over the bidisk

2012 ◽  
Vol 274 (3-4) ◽  
pp. 885-903 ◽  
Author(s):  
Kei Ji Izuchi ◽  
Kou Hei Izuchi ◽  
Yuko Izuchi
Keyword(s):  
Hardy Space ◽  
Invariant Subspaces ◽  
Backward Shift

Noncommutative Function-Theoretic Operator Theory and Applications

2021 ◽  
Author(s):  
Joseph A. Ball ◽  
Vladimir Bolotnikov
Keyword(s):  
System Theory ◽  
Hardy Space ◽  
Operator Theory ◽  
Reproducing Kernel ◽  
Invariant Subspaces ◽  
Weighted Bergman Space ◽  
Characteristic Operator ◽  
Multivariable Operator Theory ◽  
Backward Shift ◽  
Space Function

This concise monograph explores how core ideas in Hardy space function theory and operator theory continue to be useful and informative in new settings, leading to new insights for noncommutative multivariable operator theory. Beginning with a review of the confluence of system theory ideas and reproducing kernel techniques, the book then covers representations of backward-shift-invariant subspaces in the Hardy space as ranges of observability operators, and representations for forward-shift-invariant subspaces via a Beurling–Lax representer equal to the transfer function of the linear system. This pair of backward-shift-invariant and forward-shift-invariant subspace form a generalized orthogonal decomposition of the ambient Hardy space. All this leads to the de Branges–Rovnyak model theory and characteristic operator function for a Hilbert space contraction operator. The chapters that follow generalize the system theory and reproducing kernel techniques to enable an extension of the ideas above to weighted Bergman space multivariable settings.

scholarly journals Blaschke products and the rank of backward shift invariant subspaces over the bidisk

2011 ◽  
Vol 261 (6) ◽  
pp. 1457-1468 ◽  
Author(s):  
Kei Ji Izuchi ◽  
Kou Hei Izuchi ◽  
Yuko Izuchi
Keyword(s):  
Invariant Subspaces ◽  
Blaschke Products ◽  
Backward Shift

Rank of Finite Rudin Type Backward Shift Invariant Subspaces Over the Bidisk

2015 ◽  
Vol 11 (3) ◽  
pp. 675-705
Author(s):  
Kei Ji Izuchi ◽  
Kou Hei Izuchi ◽  
Yuko Izuchi
Keyword(s):  
Invariant Subspaces ◽  
Backward Shift
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