Nik Weaver
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Registered User
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9h |
answered | The “right” $C^*$ algebraic proof of Bott Periodicity |
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13h |
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Can an uniformly picked real number be an integer? Incidentally, the "probability zero never happens" language came not from the highly upvoted answer he refers to, but from OP's own response to it ... |
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13h |
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Can an uniformly picked real number be an integer? There are several grounds on which this question could be closed. |
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1d |
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Proof that a finitely generated projective module over a Von Neumann Regular ring is free Look in Ken Goodearl's book on von Neumann regular rings. |
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May 19 |
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Importance of separability vs. second-countability It sounds like you are asking why separability is important. Speaking from my area of expertise, I could tell you any number of basic theorems about separable C*-algebras which fail in the nonseparable case. |
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May 18 |
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Importance of separability vs. second-countability @Martin: do you wish to tell me that this simple fact is not important? |
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May 18 |
answered | Importance of separability vs. second-countability |
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May 18 |
accepted | Resolvent of Laplacian |
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May 17 |
answered | Is there any proof that you feel you do not “understand”? |
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May 14 |
answered | A space parameterizing the choices of orthonormal bases for a Hilbert space |
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May 12 |
answered | A characterization of Hilbert spaces? |
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May 8 |
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Is BV2 space closed in L2 space? Probably $S$ contains a dense subspace of $L^2$ like, say, the $C^\infty$ functions with compact support, but easy examples show that it is not all of $L^2$, so ... |
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May 7 |
accepted | Does the Border (Boundary) Points of a convex body make a concave function? |
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May 3 |
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Decidability of equality of expressions built using 1,+,-,*,/,^ That's right, I agree. |
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May 3 |
answered | Decidability of equality of expressions built using 1,+,-,*,/,^ |
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May 3 |
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Does the Border (Boundary) Points of a convex body make a concave function? @Wlodzimierz: yes. I've edited my answer to clarify this. |
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May 3 |
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Does the Border (Boundary) Points of a convex body make a concave function? deleted 17 characters in body |
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May 3 |
answered | Does the Border (Boundary) Points of a convex body make a concave function? |
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May 2 |
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Generalization of $e^{t A}$ to $e^{t^{\alpha}A}$ It isn't a one-parameter semigroup for $\alpha \neq 1$. The product law fails. |
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May 1 |
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Certain bounded linear operators on L^2 of a torus No problem, you're welcome. |
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May 1 |
accepted | Certain bounded linear operators on L^2 of a torus |
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May 1 |
answered | Certain bounded linear operators on L^2 of a torus |
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Apr 30 |
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Existence of a continuous and unbounded map $f$ with $f(f(x))=x$ Oh, I didn't notice the minus sign ... yes, that seems to work. Nice! |
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Apr 30 |
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Existence of a continuous and unbounded map $f$ with $f(f(x))=x$ You mean $i(x) = x/\|x\|^2$? Your map still seems to fix every element of the unit sphere. |
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Apr 30 |
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Existence of a continuous and unbounded map $f$ with $f(f(x))=x$ I'm baffled as to how you would use $h$ to construct the desired function $f$. |
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Apr 30 |
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Existence of a continuous and unbounded map $f$ with $f(f(x))=x$ The rest is straightforward? |
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Apr 30 |
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Existence of a continuous and unbounded map $f$ with $f(f(x))=x$ @MTS: clearly the answer is no for the weak* topology. If $f$ is weak* continuous then $f(B)$ must be compact, and it's an easy consequence of (some version of) the principle of uniform boundedness that every weak* compact set is bounded. |
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Apr 27 |
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Existence of a projection operator onto a classical set of density matrices @Sebastian: You may ask whether the two conditions I listed uniquely characterize $P$. I don't think so. For example, take $H = {\bf R}$ and $K = [0,\infty)$. Then the map I described is $P(x) = x$ if $x \geq 0$ and $P(x) = 0$ if $x < 0$. But the map $P(x) = |x|$ would also have the two listed properties. |
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Apr 26 |
accepted | Existence of a projection operator onto a classical set of density matrices |
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Apr 26 |
answered | Existence of a projection operator onto a classical set of density matrices |
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Apr 24 |
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Intuitionistic logic as quantization of classical logic? I really object to this definition of "quantization". Quantization in physics is not about going from something continuous to something discrete, it is about going from functions on a set to operators on a Hilbert space (which may or may not have a discrete spectrum). |
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Apr 24 |
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Uncountable Pre-Image Oh, one more comment. I wish I'd thought of saying this earlier. The proof that the complement of any countable subset of ${\bf R}^2$ is connected goes back to Cantor. I remember reading it in Dauben's biography. |
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Apr 24 |
awarded | ● Yearling |
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Apr 23 |
awarded | ● Enlightened |
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Apr 23 |
awarded | ● Nice Answer |
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Apr 23 |
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Uncountable Pre-Image @John: The complement of $f^{-1}(x)$ is disconnected because it is the disjoint union of two nonempty open sets, $U$ and $V$. |
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Apr 23 |
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When is the class of functions between sets a set? Read the paper more carefully. They are working with "big" loops, which are maps from "big" intervals into the space. Since there is a proper class of "big" intervals there is a proper class of "big" loops (before taking a quotient). |
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Apr 23 |
accepted | Uncountable Pre-Image |
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Apr 23 |
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Uncountable Pre-Image Also, my argument actually shows that $f^{-1}(x)$ has cardinality $2^{\aleph_0}$, for those who care about such niceties. |
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Apr 23 |
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Uncountable Pre-Image Actually, I only used the fact that the range of $f$ is open, not that $f$ is an open map. |
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Apr 23 |
answered | Uncountable Pre-Image |
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Apr 19 |
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Notation for a functional L2 matrix norm I'm not sure whether your question is appropriate for this site, but anyway your guess is unlikely to be correct (unless max of row 1 plus max of row 2 is somehow important for reasons you're not telling us). There are various ways to take the norm of a matrix, probably the most standard is the operator norm, and most likely the rest of your description is on target --- square the norm at each point, integrate, and take a square root. But context is needed to answer this question. |
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Apr 19 |
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Finding questions between functional analysis and set theory Sure, thanks for mentioning my paper. Incidentally, Ilijas gave another proof of our consistency result in his paper, and I think his proof is better. Our overall strategy seems more natural but making it work was really hard. His proof goes in an unexpected direction but it ends up being easier. |
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Apr 19 |
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Finding questions between functional analysis and set theory That paper by Farah et al. dealt with generalized Calkin algebras. The consistency of all automorphisms being inner was shown in an earlier paper by Farah alone, All automorphisms of the Calkin algebra are inner (arXiv:0705.3085). |
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Apr 18 |
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Are compact sets in a Banach lattice order bounded? No problem. Trivial in retrospect, maybe. |
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Apr 18 |
answered | Are compact sets in a Banach lattice order bounded? |
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Apr 11 |
awarded | ● Necromancer |
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Apr 6 |
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Density of smooth functions under “Hölder metric” @Yemon: ${\rm Lip}_\alpha$ consists of the functions which are Lipschitz for the metric $|s-t|^\alpha$. For this metric, every smooth function is "locally flat": we have $\frac{|f(t + h) - f(t)|}{|h|^\alpha} \to 0$ as $h \to 0$. The family of locally flat Lipschitz functions is a norm closed proper subspace of ${\rm Lip}_\alpha$ denoted ${\rm lip}_\alpha$. In fact the former is the second dual of the latter. |
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Apr 5 |
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How to refer to a theorem that you have shown to be wrong I vote for inverted commas. We label things to make them easy for the reader to find. Inverted commas preserve the exact reference while also making it crystal clear that the result is not to be trusted. |
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Apr 5 |
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Is it true that a solid, minihedral cone in infinite dimensions cannot be regular? The question is asked very well. You give the relevant definitions clearly and concisely, you explain why you are interested, and you outline what you've already tried. I agree that (3) is the natural thing to try, but I also don't see the contradiction there. |
