A Characterization of the Complemented Translation-Invariant Subspaces of H 1 (R)

1991 ◽  
Vol 323 (1) ◽  
pp. 197
Author(s):  
Dale E. Alspach
Keyword(s):  
Invariant Subspaces ◽  
Translation Invariant ◽  
Translation Invariant Subspaces

Norm One Multipliers on Subspaces of Lp

1992 ◽  
Vol 35 (2) ◽  
pp. 194-203
Author(s):  
Kathryn E. Hare
Keyword(s):  
Elementary Proof ◽  
Invariant Subspaces ◽  
Translation Invariant ◽  
Translation Invariant Subspaces

AbstractWe present a new elementary proof of the fact that a norm one multiplier ϕ on LP(T) satisfying ϕ(0) = ϕ(k) = 1 is k-periodic, and extend this result, when possible, to multipliers on translation invariant subspaces of LP. A consequence of our work is that all such multipliers on HP(T) are the restriction of a norm one multiplier on LP(T).

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