New posts in Functional Analysis

Example of function such that its each derivative and itself vanishes at 0 but any polynomial multiple of that function doesnot vanishes at infinity

Reflexivity of $(C^1([a,b]),\left\lVert \cdot\right\rVert_{\infty})$

$X^*$ is separable then $X$ is separable [Proof explanation]

Weak lower semicontinuity of functional with two arguments

Spectrum of operator on $L^2([0,1])$

Prove existence of evaluation points such that the matrix has nonzero determinant

Norms on polynomials

Kreyszig's FA Prob. $6$ section $2.8$

On constants attainable by the expression $\int_0^1xf(x)dx$

Show that $\sum_{n=1}^{\infty} \frac{(-1)^{n}}{\sqrt{n}}\sin(1 + \frac{x}{n})$ converges uniformly on $\mathbb{R}$