Infinity

### Questions (77)

 9 Completeness can be omitted from Banach Fixed Point Theorem? 8 Reason for the term “smooth” 4 $Y=${$(x_j/j):(x_j)\in l_\infty$}. Is Y closed in $l_\infty$? 3 Example of a metric. 3 $G=\{(x_n)\in l_1 : x_1 - 3x_2 = 0\}$, $f$ on G is defined by $f(x) = x_1$. Show $g(x) = (3/4)(x_1+x_2)$ is the unique Hahn-Banach extension for $f$.

### Reputation (629)

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 1 Dimension of vector space of matrices with zero row and column sum. 0 Nested sequence of closed sets 0 Example of nonexpansive mapping. 0 What is the closure of $\ell_1$ in $\ell_2$? 0 A linear operator T from an infinite dimensional complex vector space X to X which has no any eigenvalues.

### Tags (69)

 1 linear-algebra × 8 0 linear-transformations × 10 1 matrices × 2 0 general-topology × 9 0 functional-analysis × 54 0 metric-spaces × 8 0 normed-spaces × 28 0 banach-spaces × 7 0 real-analysis × 12 0 topological-vector-spaces × 6

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