List questions from lp-spaces

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List Question

How do you prove $L^{\infty}$ is a C*-algebra?

Sobolev spaces necessary and sufficient condition

Showing equivalence of weak convergence on closed and open intervals

$f_n\rightarrow f$ in $L_2$ and $f_n\rightarrow f$ in measure, then $f_n\rightarrow f$ almost uniformly?

Criteria to be in weak $L^{p}$ space

Inequality of $L^p$ norm and distribution function

Inequality of strong $L^p$ and weak $L^p$ norm on a finite set with counting measure

Finding limit of $p$-norm of succession of functions

L1 convergence and Lp bounded implies Lq convergence

how to show this function doesn't belong to Hilbert space?

the dual space of $L^p$

weak $L_p$ implies bounded integral on finite measure set

Weak $L_1$ norm is different from $L_1$ norm on a probability space

Two questions on Banach-valued spaces of integrable functions

$L^p$-space inclusions

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