Intereting Posts

Question on (Semi) Prime Counting Functions
Show a Schwartz function vanish at infinity
3-regular graphs with no bridges
what is the name of this number? is it transcendental?
Is this true: any bipartite graph with unbalanced vertex parity is not Hamiltonian?
If $K$ is compact, then $C(K,\mathbb{R}^n)$ is a Banach space under the norm $\|f\|=\sup_{x\in K} \|f(x)\|$
What are applications of rings & groups?
GP 1.3.9(b) Every manifold is locally expressible as a graph.
Prove that G is a cyclic group
Math competition problem, prove that $\int_{-\infty}^\infty e^{-\pi x^2 \left(\frac{\alpha +x}{\beta +x}\right)^2}dx=1~$ for $~0<\beta<\alpha$.
Prove that a straight line is the shortest distance between two points?
The height of a principal prime ideal
union of two independent probabilistic event
Prime number generator, how to make
Closed space curves of constant curvature

Let $A$ and $B$ be closed operators on a (separable complex) Hilbert space with dense domains $D(A)$ and $D(B)$ respecitvely. Then, we may define the operator $A+B$ on $D(A)\cap D(B)$. In general, we have no reason to believe that this operator will be closed, which begs the question, is it closable?

I hope I’m not being an idiot again. . . Any ideas?

- Quotient space and continuous linear operator.
- An approximate eigenvalue for $ T \in B(X) $.
- Urysohn's function on a metric space
- An inequality in the proof of characterization of the $H^{-1}$ norm in Evans's PDE book
- Weak convergence implies uniform boundedness
- The dual space of $c$ is $\ell^1$

- Can a strictly increasing convex function $F$ meet a line segment in 3 places, without being linear?
- Weak convergence of a sequence of characteristic functions
- Weak convergence on a dense subset of test functions
- A vector without minimum norm in a Banach space
- Topologies of test functions and distributions
- How to show pre-compactness in Holder space?
- Is the weak topology sequential on some infinite-dimensional Banach space?
- Do the two limits coincide?
- Differentiation operator is closed?
- How do you show that $l_p \subset l_q$ for $p \leq q$?

On $\ell^2$, define $A$ and $B$ by $(Ax)_n = -(Bx)_n = n^2 x_n$ for $n > 1$, $(A x)_1 = \sum_{n=1}^\infty n x_n$ and $(B x)_1 = 0$, with $D(A) = D(B) = \{x: \sum_{n =1}^\infty

n^4 |x_n|^2 < \infty \}$. Then if I’m not mistaken $A$ and $B$ are closed but $A + B$ is not closable, e.g. (with $e_n$ the standard unit vectors) $\lim_{n \to \infty} e_n/n =0$ while $(A + B) e_n/n = e_1$.

- Intersection of Dense Sets
- an homeomorphism from the plane to the disc
- Constructor theory distinguishability
- Nonstandard models of Presburger Arithmetic
- How can we show that $(I-A)$ is invertible?
- Question regardles primes and the fundamental theorem of arithmetic
- Gödel's Incompleteness Theorem – Diagonal Lemma
- How to find the complex roots of $y^3-\frac{1}{3}y+\frac{25}{27}$
- Prove that $\def\Aut{\operatorname{Aut}}\Aut(\mathbf{Z_{n}})\simeq \mathbf{Z_{n}^{*}}$
- Ramanujan Summation
- point deflecting off of a circle
- Can $\{(f(t),g(t)) \mid t\in \}$ cover the entire square $ \times $ ?
- Prove that $\lim\limits_{n\to\infty}1 + \frac{1}{1!} + \frac {1}{2!} + \cdots + \frac{1}{n!}\ge\lim\limits_{n\to\infty}(1+\frac{1}{n})^n$
- What is a topology?
- Simple upper bound for $\binom{n}{k}$