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Continuous dual space

{title2=$T^*:Y^*\to X^*$}

= Banach-space adjoint
{c}
{synonym}

= Dual map of bounded linear operator
{synonym}

For a <bounded linear operator> $T:X\to Y$, its transpose or dual map is $T^*:Y^*\to X^*$ defined by
$$
(T^*y^*)(x)=y^*(Tx).
$$
It satisfies $\lVert T^*\rVert=\lVert T\rVert$.


Transpose of a bounded linear operator

codex/banach-space-adjoint

codex/dual-map-of-bounded-linear-operator

Transpose of a bounded linear operator ( $T^{} : Y^{} \to X^{*}$ )

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Transpose of a bounded linear operator (T∗:Y∗→X∗)

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Transpose of a bounded linear operator ( $T^{} : Y^{} \to X^{*}$ )

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