# Tagged Questions

Functional analysis is the study of infinite-dimensional vector spaces, often with additional structures (inner product, norm, topology), with typical examples given by function spaces. The subject also includes the study of linear and non-linear operators on these spaces, as well as measure, ...

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### Absolute Convergence of a Series defined as a Cauchy Sequence

So the question I'm answering is "Suppose (X, || ||) is a normed space. Show that X is complete iff every absolutely convergent series in X converges on an element of X." The first half was simple (...
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### Why should the map $-\Delta^{-1}$ continuous?

I'm reading an article by Wei-Ming Ni about the existence of solutions for the elliptic problem $$\Delta u +|x|^\lambda |u|^\tau =0,$$ in the unit ball $\Omega$ in dimension $>2$. I'm looking for ...
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### How does this follow from the theorem?[normed linear space]

I have this theorem: Let X and Y be normed linear spaces and let $T:X\rightarrow Y$ be a linear transformation. The following are equivalent: a. T is uniformly continuous. b. T is ...
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### Are lattice operations in set of orthogonal projections in Hilbert space continous?

Let $H$ be Hilbert space and denote set of all orthogonal projections in $H$ by $\Pi$. Then $\Pi$ can be given structure of a lattice. We partially order it by declaring $P \leq Q$ if $Q-P$ is ...
### Is $B(H)$ the weak-$*$ closure of $K(H)$?
I am getting the following result: If $H$ is a Hilbert space, then the weak-$*$ closure of $K(H)$, the space of compact operators on $H$, is $B(H)$, the space of bounded operators on $H$. Is this ...