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Ali Taghavi
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Ali Taghavi
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Assume that $X$ and $Y$ are two Banach spaces and $T:X\to Y$ is a bounded surjective linear operator.

A consequence of the Michael selection theorem is that:"There is a continuous function $g:Y\to X$ such that $T\circ g=Id_{Y}$".

Can we always find a linear map $g$ as above?

Assume that $X$ and $Y$ are two Banach spaces and $T:X\to Y$ is a bounded surjective operator.

A consequence of the Michael selection theorem is that:"There is a continuous function $g:Y\to X$ such that $T\circ g=Id_{Y}$".

Can we always find a linear map $g$ as above?

Assume that $X$ and $Y$ are two Banach spaces and $T:X\to Y$ is a bounded surjective linear operator.

A consequence of the Michael selection theorem is that:"There is a continuous function $g:Y\to X$ such that $T\circ g=Id_{Y}$".

Can we always find a linear map $g$ as above?

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Ali Taghavi
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  • 31
  • 123

A linear consequence of the Michael selection theorem

Assume that $X$ and $Y$ are two Banach spaces and $T:X\to Y$ is a bounded surjective operator.

A consequence of the Michael selection theorem is that:"There is a continuous function $g:Y\to X$ such that $T\circ g=Id_{Y}$".

Can we always find a linear map $g$ as above?