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Show that the infimum of $T(v)=\|v-u\|_\infty$ is not attained

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#functional-analysis #optimization #banach-spaces
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Characterization of Hilbert spaces

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#functional-analysis #banach-spaces #hilbert-spaces
117
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If $X$ is a separable Banach space $ \Rightarrow$ $ X=\overline{\cup_{n=1}^{\infty} X_n}$ where $\dim X_n=n$

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#functional-analysis #banach-spaces
208
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If A is a balanced subset $\Longrightarrow$ conv$(A)$ is balanced

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#functional-analysis #banach-spaces
184
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Distance from a point to a plane in normed spaces

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#functional-analysis #banach-spaces #normed-spaces
661
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Show that ($\ell^1$, $\|\cdot\|_1$) is complete

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#sequences-and-series #convergence-divergence #banach-spaces
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Uncountable basis and separability

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#functional-analysis #banach-spaces #hilbert-spaces
161
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Need help with one basic result of linear operators on Banach spaces

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#functional-analysis #banach-spaces
95
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Distance of a point from a subspace vs. diameter

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#geometry #functional-analysis #banach-spaces #normed-spaces
38
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Why if $\rho(I_{\mathfrak{X}} - YA)<1$ then $YA$ is invertible on the $R(YA)$?

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#functional-analysis #banach-spaces
100
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A basic question on the linear operators on Banach space

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#functional-analysis #banach-spaces
905
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Bounded operator and dense sets

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#operator-theory #banach-spaces
180
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Banach space integral via defining it in $X^{**}$ and then proving it's in $X$

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#functional-analysis #integration #banach-spaces #lebesgue-integral #vector-analysis
593
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What is a decreasing scale of Banach spaces?

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#functional-analysis #banach-spaces #normed-spaces #self-learning
139
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Do I have a Banach space given the following norm?

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#banach-spaces #normed-spaces

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