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correct Hölder's in title etc.
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Jukka Kohonen
Jukka Kohonen
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Holders Hölder's inequality for Hilbert Schmidt-Schmidt operators which are also trace class

DoesDo Hilbert-Schmidt operators which are also trace class, satisfy HoldersHölder's inequality? That is, we have two Hilbert Schmidt-Schmidt operators $A$ and $B$. Is the following true? $$\langle A, B \rangle \leq \lVert A \rVert_p \lVert B \rVert_q $$

such thatwhen $1/p + 1/q = 1$. Specifically, is it true for $p=1, q=\infty$$p=1$, $q=\infty$?

Holders inequality for Hilbert Schmidt operators which are also trace class

Does Hilbert-Schmidt operators which are also trace class, satisfy Holders inequality? That is, we have two Hilbert Schmidt operators $A$ and $B$. Is the following true? $$\langle A, B \rangle \leq \lVert A \rVert_p \lVert B \rVert_q $$

such that $1/p + 1/q = 1$ Specifically, is it true for $p=1, q=\infty$?

Hölder's inequality for Hilbert-Schmidt operators which are also trace class

Do Hilbert-Schmidt operators which are also trace class, satisfy Hölder's inequality? That is, we have two Hilbert-Schmidt operators $A$ and $B$. Is the following true? $$\langle A, B \rangle \leq \lVert A \rVert_p \lVert B \rVert_q $$

when $1/p + 1/q = 1$. Specifically, is it true for $p=1$, $q=\infty$?

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Another Grad student
Another Grad student
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Holders inequality for Hilbert Schmidt operators which are also trace class

Does Hilbert-Schmidt operators which are also trace class, satisfy Holders inequality? That is, we have two Hilbert Schmidt operators $A$ and $B$. Is the following true? $$\langle A, B \rangle \leq \lVert A \rVert_p \lVert B \rVert_q $$

such that $1/p + 1/q = 1$ Specifically, is it true for $p=1, q=\infty$?