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Injective compact linear operator from infinite dimensional normed space

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#normed-spaces #compact-operators
32
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Existence of compact operator with eigenvelues determined by a given sequence

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#functional-analysis #compact-operators
49
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Brezis' exercise 6.13.1: $\forall \varepsilon>0\,\exists C_\varepsilon > 0$ s.t. $|Tu|_F \le \varepsilon |u|_E + C_\varepsilon |u|$

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#functional-analysis #solution-verification #banach-spaces #compact-operators
33
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Proof of Ringrose Theorem

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#functional-analysis #compact-operators
32
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Brezis' exercise 6.18.1: does $S_r$ or $S_{\ell}$ belong to $\mathcal{K}(E)$?

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#functional-analysis #solution-verification #banach-spaces #lp-spaces #compact-operators
45
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Strictly positive compact operator commuting with a given Fredholm operator

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#functional-analysis #compact-operators #k-theory #unbounded-operators
77
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Trace theorem for Bochner space.

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#real-analysis #functional-analysis #sobolev-spaces #compact-operators #bochner-spaces
80
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Atkinson Theorem for unbounded Fredholm Operators

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#functional-analysis #operator-theory #compact-operators
42
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Is it true that $T$ is surjective IFF $T-K$ is surjective?

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#functional-analysis #operator-theory #banach-spaces #compact-operators
76
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Compact operator in $\ell_2$

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#functional-analysis #hilbert-spaces #compact-operators
65
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Conditions for an integral operator to be a compact operator on L^2(R)

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#functional-analysis #analysis #operator-theory #compact-operators #integral-operators
40
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Brezis' exercise 6.20.1: prove that $T \in \mathcal{K}(E)$

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#functional-analysis #solution-verification #banach-spaces #lp-spaces #compact-operators
102
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Does $x_n \rightharpoonup 0$, where $\|x_n \| \leq 1$ imply $Ax_n\rightarrow 0$, when $A$ is a compact, self-adjoint projection?

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#functional-analysis #hilbert-spaces #weak-convergence #compact-operators #weak-topology
45
Views

Brezis' exercise 6.21.1: prove that $N$ is finite-dimensional

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#functional-analysis #solution-verification #banach-spaces #compact-operators
45
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Eigenvalues of a resriction of a compact operator

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#functional-analysis #hilbert-spaces #spectral-theory #projection #compact-operators

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