Reducing subspaces for the product of a forward and a backward operator-weighted shifts

2021 ◽  
Vol 501 (2) ◽  
pp. 125206
Author(s):  
Xu Tang ◽  
Caixing Gu ◽  
Yufeng Lu ◽  
Yanyue Shi
Keyword(s):  
Weighted Shifts ◽  
Reducing Subspaces

Unitary equivalence and reductibility or invertibly weighted shifts

1971 ◽  
Vol 5 (2) ◽  
pp. 157-173 ◽  
Author(s):  
Alan Lambert
Keyword(s):  
Hilbert Space ◽  
Sufficient Conditions ◽  
Bounded Sequence ◽  
Complex Hilbert Space ◽  
Weighted Shifts ◽  
Infinite Dimensional ◽  
Reducing Subspaces ◽  
Positive Weights ◽  
Completely Reducible ◽  
Necessary And Sufficient

Let H be a complex Hilbert space and let {A1, A2, …} be a uniformly bounded sequence of invertible operators on H. The operator S on l2(H) = H ⊕ H ⊕ … given by S〈x0, x1, …〉 = 〈0, A1x0, A2x1, …〉 is called the invertibly veighted shift on l2(H) with weight sequence {An }. A matricial description of the commutant of S is established and it is shown that S is unitarily equivalent to an invertibly weighted shift with positive weights. After establishing criteria for the reducibility of S the following result is proved: Let {B1, B2, …} be any sequence of operators on an infinite dimensional Hilbert space K. Then there is an operator T on K such that the lattice of reducing subspaces of T is isomorphic to the corresponding lattice of the W* algebra generated by {B1, B2, …}. Necessary and sufficient conditions are given for S to be completely reducible to scalar weighted shifts.

scholarly journals Flat phenomena of 2-variable weighted shifts

2015 ◽  
Vol 486 ◽  
pp. 234-254 ◽  
Author(s):  
Jaewoong Kim ◽  
Jasang Yoon
Keyword(s):  
Weighted Shifts

A Subnormal Completion Problem for Weighted Shifts on Directed Trees

2018 ◽  
Vol 90 (6) ◽  
Author(s):  
George R. Exner ◽  
Il Bong Jung ◽  
Jan Stochel ◽  
Hye Yeong Yun
Keyword(s):  
Weighted Shifts ◽  
Completion Problem

Hamburger-type weighted shifts: Jumping flatness and Aluthge transforms

2021 ◽  
Vol 494 (1) ◽  
pp. 124592
Author(s):  
George R. Exner ◽  
Joo Young Jin ◽  
Il Bong Jung ◽  
Ji Eun Lee
Keyword(s):  
Weighted Shifts
Sign in / Sign up

Export Citation Format

Share Document