If $V$,$W$are two inner product spaces and $L:V\to W$ is a linear map with its adjoint $L^\star$, then is there a decomposition of $W$=ker$(L^\star)$ $ \oplus $ im$(L)$ ? (It is easy that the conclusion holds if $V$ and $W$ are finite-dimensional)
The decomposition of inner product space
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linear-algebra
functional-analysis
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0I think, $L^*$ is not well definied, so you should give your definition. – 2012-04-06