In this semi-expository paper, we examine the backward shift operator

Bf := (f-f(0)/z

on the classical Hardy space Hp. Through there are many aspects of this operator worthy of study [20], we will focus on the description of its invariant subspaces by which we mean the closed linear manifolds Ɛ ⊂ Hp for which BƐ ⊂ Ɛ. When 1 < p < ∞, a seminal paper of Douglas, Shapiro, and Shields [8] describes these invariant subspaces by using the important concept of a pseudocontinuation developed earlier by Shapiro [26]. When p = 1, the description is the same [1] except that in the proof, one must be mindful of some technical considerations involving the functions of bounded mean oscillation.

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Post-print Article

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Copyright © 2005 Birkhäuser Verlag Basel.

DOI: 10.1007/3-7643-7340-7_14

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Full Citation:

Ross, William T. "The Backward Shift on Hp." Operator Theory: Advances and Applications Selected Topics in Complex Analysis 158 (2005): 191-211. doi:10.1007/3-7643-7340-7_14.