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shift operators in 
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(Definition)
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Let
 be
 or
 , and let $1\le p\le \infty$ , let
 be as in the parent entry.
The right and left shift operators
 as defined as follows. For
 , $$ S_r(a)=(0,a_1, a_2, \ldots) $$ and $$ S_l(a)=(a_2, a_3, \ldots). $$
- $S_l \circ S_r$ is the identity, but $S_r\circ S_l$ is not.
- $S_r$ is an isometry; $\Vert S_r(a)\Vert = \Vert a \Vert$ , and $\Vert S_l(a)\Vert_p \le \Vert a\Vert$ . Both shift operators are therefore bounded (and continuous).
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"shift operators in  " is owned by matte.
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Cross-references: continuous, bounded, isometry, identity, operators, right, parent
This is version 1 of shift operators in  , born on 2005-05-21.
Object id is 7092, canonical name is ShiftOperatorsInEllp.
Accessed 1240 times total.
Classification:
| AMS MSC: | 46B99 (Functional analysis :: Normed linear spaces and Banach spaces; Banach lattices :: Miscellaneous) | | | 54E50 (General topology :: Spaces with richer structures :: Complete metric spaces) |
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Pending Errata and Addenda
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