1
vote
1answer
27 views

Inequality norms

Let $A$ be a bounded linear operator on a Banach space $X$. Can we show that for an arbitrary $n \in \mathbb{N}$ and $x \in X$ such that $\|x\|_X \geq 1$ we have that $$\|A^n x \| \leq \|Ax\|^n.$$ ...
3
votes
2answers
224 views

Inequality for a selfadjoint operator on Hilbert space

Let $T$ be a (possibly unbounded) selfadjoint nonnegative operator on a Hilbert space $H$ with domain $D$. Assume that $\langle T u, u \rangle \leq c$ for some $c>0$ and some $u\in D$. I found ...
12
votes
1answer
278 views

Singular-value inequalities

This is my question: Is the following statement true ? Let $H$ be a real or complex Hilbertspace and $R,S:H \to H$ compact operators. For every $n\in\mathbb{N}$ the following inequality holds: ...