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1d

comment 
Do nonnormal states exist in the Solovay model?
This should be a nonnormal state on a nonseparable Hilbert space in the Solovay model : Let $H = l^2([0,1])$ and $\lbrace e_x : x \in [0,1] \rbrace$ an orthonormal basis of H . Then $f$ defined by $f(A) = \int_0^1 <e_x, A e_x> dx$ for $A \in B(H)$ is a nonnormal state . 
1d

comment 
Do nonnormal states exist in the Solovay model?
@Ashutosh : to lo.logic + math.physics : See the comments to Arnold Neumaiers answer in physicsoverflow.org/31006/whyisntthepathintegralrigorous 
2d

comment 
Do nonnormal states exist in the Solovay model?
@Ashutosh : Yes, at least for separable Hilbert spaces. 
2d

comment 
Do nonnormal states exist in the Solovay model?
@Ashutosh : According to Gleasons theorem for separable Hilbert spaces of dimension other than 2 states correspond to finitely additive measures on pairwise orthogonal projections but normal states correspond to sigmafinite measures, see ncatlab.org/nlab/show/Gleason%27s+theorem . 
2d

comment 
Do nonnormal states exist in the Solovay model?
@Asaf Karagila : All states have norm 1, but nonnormal states are discontinous in some other topologies (e.g. ultraweak), see ncatlab.org/nlab/show/state+on+an+operator+algebra . 
2d

asked  Do nonnormal states exist in the Solovay model? 
May 9 
comment 
How to prove this determinant is positive?
@TerryTao : $T$ could also be of the form $\begin{pmatrix} A & A B \\ 0 & A^{*1}\end{pmatrix}$, where $B^{*} =  B$ . 
May 3 
comment 
How to prove this determinant is positive?
@GH from MO : ok, my mistake was that the Baker–Campbell–Hausdorff formula is not always convergent. 
May 3 
revised 
How to prove this determinant is positive?
added 67 characters in body 
May 3 
comment 
How to prove this determinant is positive?
@Christian Remling choose $M = \left[\begin{matrix}0 & \pi & 0 & 0\\ \pi & 0 & 0 & 0\\0 & 0 & 0 & \pi\\0 & 0 &  \pi & 0\end{matrix}\right]$ 
May 3 
comment 
How to prove this determinant is positive?
@user23765 : This formular doesn't evaluate log(1), it evaluates the log auf the product of 2 exponentials, which is simply $X + Y$ in the commuting case but more complicated in the noncommuting case. But the result is still real, if X and Y are real. 
May 3 
comment 
How to prove this determinant is positive?
@user23765 : See en.wikipedia.org/wiki/… : From the Baker–Campbell–Hausdorff formula it follows, that a real M exists. 
May 3 
revised 
How to prove this determinant is positive?
added 1 character in body 
May 3 
answered  How to prove this determinant is positive? 
May 3 
comment 
How to prove this determinant is positive?
I think T is not connected to the identity (the log T I calculated is complex). This means that it is no counterexample. 
May 1 
comment 
Does this recursion preserve monotonicity? (was: A nice problem that I am unable to solve)
$f_n(x)$ seems to be concave on $[0,1]$, or not ? 
Feb 25 
awarded  Necromancer 
Jan 6 
comment 
Examples of potentials for which Schrödinger equation lacks discrete points in continuous spectrum
Maybe this makes sense in the rigged Hilbert space approach ? 
Jan 6 
comment 
On $e^{\pi\sqrt{4\cdot163}}$ and unusual connections
for BekensteinHawking entropy see en.wikipedia.org/wiki/Black_hole_thermodynamics 
Nov 27 
comment 
translation invariance of the Laughlin wave function
@Carlo Beenakker : What about Laughlins wavefunction on the sphere ? In this case Laughlins wavefunction is SU(2) invariant. 