shift operators in p

Let 𝔽 be or , and let 1p, let p(𝔽),p be as in the parent entry.

The right and left shift operators Sr,Sl:p(𝔽)p(𝔽) as defined as follows. For a=(a1,a2,)p(𝔽),





  1. 1.

    SlSr is the identity, but SrSl is not.

  2. 2.

    Sr is an isometry; Sr(a)=a, and Sl(a)pa. Both shift operators are therefore bounded (and continuousMathworldPlanetmath).

Title shift operators in p
Canonical name ShiftOperatorsInellp
Date of creation 2013-03-22 15:17:40
Last modified on 2013-03-22 15:17:40
Owner matte (1858)
Last modified by matte (1858)
Numerical id 4
Author matte (1858)
Entry type Definition
Classification msc 46B99
Classification msc 54E50