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, ...

21 views

A question on uniform algebras

Let $A$ be a uniform algebra on a compact metric space $X$ Why the necessary condition for $A$ to be $C(X)$(the algebra of all complex-valued continuous functions on $X$) is that the maximal ideal ...
29 views

84 views

Supremum of absolute value of the Fourier transform equals $1$, and it is attained exactly at $0$

Suppose that $f \in L^1(\mathbb{R}^n)$, $f \ge 0$, $\|f\|_{L^1} = 1$. How do I see that $\sup_{\xi\in\mathbb{R}^n} |\mathcal{F}(f)(\xi)| = 1$, and it is attained exactly at $0$?
38 views

An exemple of strict inequality for reverse inequality Minkowski for space $L^p$, $0 < p <1$

Let be $0<p<1$. Suppose that we know that $$\bigg(\int (u + v)^p\bigg)^{1/p} \geq \bigg(\int (u)^p\bigg)^{1/p} +\bigg(\int (v)^p\bigg)^{1/p}$$ for all $u,v \geq 0$ in $L^p$. I need find an ...
23 views

19 views

Is $f$ is closed equivalent to the graph of $f$ is closed when $f$ is linear

Suppose $X,Y$ are topological vector spaces, $f:X\rightarrow Y$ is a linear map, is that true that two of the following are equivalnet: 1.$f$ is closed 2.The graph of $f$ is closed. What if $X,Y$ ...
31 views