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"If he had been a great and wise philosopher... he would now have comprehended that Work consists of whatever a body is obliged to do, and that Play consists of whatever a body is not obliged to do. And this would help him to understand why constructing artificial flowers or performing on a tread-mill is work, while rolling ten-pins or climbing Mont Blanc is only amusement."

-- from The Adventures of Tom Sawyer by Mark Twain --


22h
reviewed Leave Open Which journals publish research announcements?
1d
comment Uniformly small sums of roots of unity
Just to clarify: do you mean that for each such $k$ there exists an $S$ of cardinality $k$, etc?
1d
comment HISTORY OF MATHEMATICS
@JohnStillwell +1000 if I could
2d
reviewed Reject Bijection between dominant rational maps and morphisms of function fields?
Jul
1
comment A question on an argument in Woronowicz’s paper on the compact quantum group $ {\text{SU}_{q}}(2) $
[deleted comment caused by not reading properly; sorry]
Jul
1
comment Question on real polynomial in projective space
I'm voting to close this question for the reason in my previous comment
Jul
1
comment Question on real polynomial in projective space
I don't think MO should be a substitute for the process of graduate instruction
Jul
1
revised Can phase significantly concentrate a function's spectrum?
deleted 81 characters in body
Jul
1
comment Can phase significantly concentrate a function's spectrum?
@WillSawin Good point. I'll update my answer
Jun
30
answered Can phase significantly concentrate a function's spectrum?
Jun
29
comment 'Test Functions' to Lower Bound the Norm of Elements of Dual Quantum Group
OK, I've cobbled something together. Apologies for any earlier confusion
Jun
29
answered 'Test Functions' to Lower Bound the Norm of Elements of Dual Quantum Group
Jun
28
comment 'Test Functions' to Lower Bound the Norm of Elements of Dual Quantum Group
Correction to my earlier comment: while this result is in Dixmier's book, the "Section V.2" actually refers to Volume 1 of Takesaki's Theory of Operator Algebras
Jun
28
comment 'Test Functions' to Lower Bound the Norm of Elements of Dual Quantum Group
It's the given, usual norm on $M$, and you want the formula I wrote, not the formula you wrote. The formula you wrote doesn't look right even in the simple case of $M=L^\infty[0,1]$ and $\tau(f)=\int_0^1 f(t)dt$
Jun
27
comment 'Test Functions' to Lower Bound the Norm of Elements of Dual Quantum Group
It's in Dixmier's book on von Neumann algebras. I don't have a copy to hand but I once had to cite this fact and if I got it right, then it is in Section V.2 of his book (French version, but presumably also the English translation). I suspect it might originally be due to I. Segal back in the 1950s?
Jun
27
comment 'Test Functions' to Lower Bound the Norm of Elements of Dual Quantum Group
Hmm, well perhaps I have misunderstood your question, but if $\tau$ is a faithful normal trace on a von Neumann algebra $M$, then IIRC $\tau((x^*x)^{1/2})$ is equal to the supremum of $|\tau(xy)|$ as $y$ runs over all elements in unit ball of M
Jun
27
comment 'Test Functions' to Lower Bound the Norm of Elements of Dual Quantum Group
I find your question somewhat unclear. Are you merely asking for a way to express the noncommutative L^1-norm given by a tracial state as a supremum using the natural pairing? (Your definition of the 1-norm seems to be the usual one if the Haar state is tracial, as it is for Kac examples, but I am not sure it is the correct definition in the non-tracial case)
Jun
27
comment Is :$\frac{\Bbb d}{\Bbb d x}$ a chaotic operator in infinite-dimensional Hilbert space?
@AndrásBátkai perhaps the OP had something like link.springer.com/article/10.1007%2FBF01299846 in mind?
Jun
27
comment Is :$\frac{\Bbb d}{\Bbb d x}$ a chaotic operator in infinite-dimensional Hilbert space?
[deleted over-hasty comment] I still feel this question should have been left on MSE and is not appropriate for MO
Jun
27
comment A Paradox by a Variant of Von Neumann's coin toss
They're not puns.