Intereting Posts

How to calculate the sumation of a function in one step?
Arrange $n$ people so that some people are never together.
“Normalize” values to sum 1 but keeping their weights
Evaluation of $\lim\limits_{n\to\infty} (\sqrt{n^2 + n} – \sqrt{n^3 + n^2}) $
Is this a valid use of l'Hospital's Rule? Can it be used recursively?
Fixed point property of Cayley plane
Lipschitz Smoothness, Strong Convexity and the Hessian
Rewrite an Integeral according to elliptic function of the second kind
Prove that $R \otimes_R M \cong M$
$T$ is continuous if and only if $\ker T$ is closed
Are $\sigma$-algebras that aren't countably generated always sub-algebras of countably generated $\sigma$-algebras?
Find Minimum value of $P=\frac{1}{1+2x}+\frac{1}{1+2y}+\frac{3-2xy}{5-x^2-y^2}$
Conformal map between annulii
Prove $\int_0^{2\pi}\frac{3a\sin^2\theta}{(1-a\cos \theta)^4}\mathrm{d}\theta = \int_0^{2\pi}\frac{\cos \theta}{(1-a\cos \theta)^3}\,\mathrm{d}\theta$
probability of rolling at least $n$ on $k$ 6-sided dice

What is an example of a $C^{*}$ algebra such that the span of nilpotent elements is not a sub vector space of the span of commutator elements.

Obviously any such $C^{*}$ algebra would be a counter example to the question $2$ of the following MO post:

https://mathoverflow.net/questions/231328/the-saturation-of-murray-von-neumann-relation

- Why is $\overline{B(l^2)\odot B(l^2)}^{\| \enspace \|_{op}}\neq B(l^2\otimes l^2)?$
- For a hermitian element $a$ in a $C^*$-algebra, show that $\|a^{2n}\| = \|a\|^{2n}$
- What does a homomorphism $\phi: M_k \to M_n$ look like?
- Properties of a $B^\ast$-algebra
- If a sub-C*-algebra does not contain the unit, is it contained in a proper ideal?
- Essential ideals

I know that every stable $C^{*}$ algebra or every properly infinite $C^{*}$ algebra can be generated by nilpotent elements. But it seems that such algebras do not admit “nice” trace. However for my purpose an algebraic trace(A linear functional which vanishs on commutators) is sufficient(not necessarily positive or bounded trace)

- A function that is $L^p$ for all $p$ but is not $L^\infty$?
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- Show that the dual norm of the spectral norm is the nuclear norm
- Distinguishing between symmetric, Hermitian and self-adjoint operators
- Topology on the space of universally integrable functions
- Compactness in $L^1$
- Prove that if f in $C(X \times Y)$ then there exists functions.
- Is there a concept of a “free Hilbert space on a set”?
- Bounded data means bounded solution to parabolic PDE
- Fredholm Alternative as seen in PDEs, part 1

- Maximum amount willing to gamble given utility function $U(W)=\ln(W)$ and $W=1000000$ in the game referred to in St. Petersberg's Paradox?
- Sums of rising factorial powers
- First-order logic: nested quantifiers for same variables
- Splitting field of $x^n-a$ contains all $n$ roots of unity
- How to translate set propositions involving power sets and cartesian products, into first-order logic statements?
- Find the acute angle $x$ for $\tan x = \tan(x+10^\circ)\tan(x+20^\circ)\tan(x+30^\circ)$.
- A function for which the Newton-Raphson method slowly converges?
- Is the Galois group associated to a random polynomial solvable with probability 0?
- Closed-forms for several tough integrals
- What is the most elegant and simple proof for the law of cosines?
- How to calculate the integral of $x^x$ between $0$ and $1$ using series?
- Borel set preserved by continuous map
- Differentiation with respect to a matrix (residual sum of squares)?
- Theorem 3.37 in Baby Rudin: $\lim\inf\frac{c_{n+1}}{c_n}\leq\lim\inf\sqrt{c_n}\leq\lim\sup\sqrt{c_n}\leq \lim\sup\frac{c_{n+1}}{c_n}$
- Combinatorics-N boys and M girls are learning acting skills from a theatre in Mumbai.