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If an $n$ by $n$ complex matrix $A$ has trace zero, then it is a commutator, which means that there are $n$ by $n$ matrices $B$ and $C$ so that $A= BC-CB$. What is the order of the best constant $\... 1answer 563 views ### Operator norms of circulant matrices The definition and basic properties of circulant matrices can be found here: http://en.wikipedia.org/wiki/Circulant_matrix. For complex numbers$a_1,\ldots,a_n$, I will use the notation$$\mbox{... 1answer 774 views ### Kaplansky's conjecture and Martin's axiom Recall Kaplansky's conjecture which states that every algebra homomorphism from the Banach algebra C(X) (where X is a compact Hausdorff topological space) into any other Banach algebra, is ... 2answers 656 views ### C*-algebras with bizzarre structure of projections This is probably well-known to the experts but I could not find any answer neither in my head nor in the literature: Is there a (unital) C*-algebra such that its projections do not form a lattice (... 2answers 331 views ### Terminology: Banach spaces equipped with continuous associative product? This is admittedly a low-interest question mathematically, and is arguably a question I could resolve if I had time over the next few days to go and look through a large number of the Banach algebra/... 2answers 176 views ### Root of positive function in Fourier algebra Let$G$be a locally compact group, let$A(G)$be the Fourier algebra of$G$. We think of$A(G)$as a subalgebra of$C_0(G)$. Question 1: Let$f\in A(G)$be a function that is pointwise positive. ... 2answers 607 views ### Banach algebraic proof of the Borsuk Ulam theorem I am wondering whether there exists a proof of the classical Borsuk Ulam theorem for the Euclidean n-sphere,$n>2$that is based only on the theory of Banach algebras. I checked on MR but had no ... 1answer 277 views ### characterization of commutative Banach algebras Let$A$be a Banach algebra with the following property: For every two nets$ x_{\alpha}$and$y_{\alpha}$in$A$,$x_{\alpha}y_{\alpha}$converges if and only if$y_{\alpha}x_{\alpha}$converges. ... 1answer 239 views ###$Z_{2}$- graded structures for$C_{red} ^{*} (F_{2})$Let$F_{2}$be the free group with two generators. Then$F_{2}=\{\text{odd words}\}\sqcup\{\text{even words}\}$. This gives us a$Z_{2}$graded structure for$C^{*}_{red} (F_{2})$, in a natural way. ... 0answers 180 views ### A noncommutative analogy of the tube lemma Assume that$A$and$B$are two unital commutative Banach algebras. Assume that$\phi \in \mathcal{M} (A)$is an element of the maximal Ideal space. Define$\alpha: A\hat{\otimes} B \to \mathbb{C}\...
Let $A,B$ be Banach algebras and $A\hat{\otimes}B$ be projective tensor product of them. Let $S$ be an ideal of $A\hat{\otimes}B$. Are there ideals $I$ of $A$ and $J$ of $B$ such that \$S=I\hat{\...