What does the definition of a space + an element mean, for example $f+L^2$.
Is this the same as the direct sum $\{f\}+L^2$, e.g. $$\{f+g|g\in L^2\}$$
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1What's the context? I'm inclined to say yes it's that set (not sure why you call it a direct sum since ${f}$ is not a vector space) without any context. – Osama Ghani Jun 25 '20 at 00:42
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@OsamaGhani The context is functional analysis and pdes. – Tony Jun 25 '20 at 00:52
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@Tony The broad context is kind of clear from writing $L^2$, but what is a specific instance, where you found that notion confusing? eg something like „let $f+L^2$ be an element in $L^3(X)/L^2(X)$ (assuming $X$ is wellbehaved https://math.stackexchange.com/questions/66029/lp-and-lq-space-inclusion). Please consider adding this type of context to your question as it makes it easier for others to understand your problem and answer the question in your terms. – Jonas Linssen Jun 25 '20 at 07:52