scholarly journals Shift reducing subspaces and irreducible-invariant subspaces generated by wandering vectors and applications

2004 ◽  
Vol 65 (6) ◽  
pp. 607-627 ◽  
Author(s):  
Carlos S. Kubrusly ◽  
Nhan Levan
Keyword(s):  
Invariant Subspaces ◽  
Reducing Subspaces ◽  
Wandering Vectors

scholarly journals On Invariant Subspaces for the Shift Operator

Symmetry ◽  
2019 ◽  
Vol 11 (6) ◽  
pp. 743
Author(s):  
Junfeng Liu
Keyword(s):  
Hardy Space ◽  
Lebesgue Space ◽  
Linear Subspace ◽  
Shift Operator ◽  
Invariant Subspaces ◽  
Closed Linear Subspace ◽  
Large Classes ◽  
Reducing Subspaces ◽  
Hyperinvariant Subspaces ◽  
And Function

In this paper, we improve two known invariant subspace theorems. More specifically, we show that a closed linear subspace M in the Hardy space H p ( D ) ( 1 ≤ p < ∞ ) is invariant under the shift operator M z on H p ( D ) if and only if it is hyperinvariant under M z , and that a closed linear subspace M in the Lebesgue space L 2 ( ∂ D ) is reducing under the shift operator M e i θ on L 2 ( ∂ D ) if and only if it is hyperinvariant under M e i θ . At the same time, we show that there are two large classes of invariant subspaces for M e i θ that are not hyperinvariant subspaces for M e i θ and are also not reducing subspaces for M e i θ . Moreover, we still show that there is a large class of hyperinvariant subspaces for M z that are not reducing subspaces for M z . Furthermore, we gave two new versions of the formula of the reproducing function in the Hardy space H 2 ( D ) , which are the analogue of the formula of the reproducing function in the Bergman space A 2 ( D ) . In addition, the conclusions in this paper are interesting now, or later if they are written into the literature of invariant subspaces and function spaces.

Invariant Subspaces on KPC-Hypergroups

2019 ◽  
Vol 15 (1) ◽  
pp. 122-130
Author(s):  
Laszlo Szekelyhidi ◽  
◽  
Seyyed Mohammad Tabatabaie ◽  
Keyword(s):  
Invariant Subspaces

Invariant Subspaces

1973 ◽  
Author(s):  
Heydar Radjavi ◽  
Peter Rosenthal
Keyword(s):  
Invariant Subspaces
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