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Q&A for professional mathematicians
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Let $A$ be a $C^*$-algebra and $(a_{ij}) \in M_n(A)$ be a positive matrix. Does there exist a constant $C \ge 0$ (not depending on the $a_{ij}$) such that $$\lVert(a_{ij})\rVert \le C \Bigl\lVert\s...
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Hottest Questions Today - MathOverflow
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0 days
Upper-bounded version of the Gale-Ryser theorem
The standard Gale-Ryser theorem is for the existence of a $(0,1)$-matrix given exact row sums $R = (r_1, \dots, r_K)$ and exact column sums $C = (c_1, \dots, c_M)$. What if we relax the column sums and want at most those $c_j$ instead of exactly those...
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Set of maximals of a closed and hereditary set as a tree over N
Let $G$ be a hereditary and closed set of $2^{\Bbb N}$. And let $G^\max$ be the set of maximals of $G$ with inclusion. This set is $G_\delta$ in $2^{\Bbb N}$. That means I can see it as a closed set of the Baire space $\Bbb{N^N}$, that is, as $[T]$ for...
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Decision problem for finite (unordered) trees
One of the strongest results on the decidability of theories is Rabin's Tree Theorem. One way to state it is the following: tThe problem of deciding whether a sentence on the monadic second order (MSO) theory of graphs has finite tree model is decidable...
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Stalkwise isomorphic etale sheaves implies locally isomorphism
I was reading the proof of Milne étale cohomology on Brauer groups IV.2.1. Prove that if $A\otimes k(x)$ is a central simple algebra over $k(x)$ for all $x$. Then there exists (finite) etale covering $(U_i)$ such that $A|_{U_i}\cong M_{n_i}(U_i)$ for...
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