Angelo Lucia
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 Apr4 comment Expanding information capacity of Gaussian Channel Could you please clarify your notation? I suppose $I(\cdot; \cdot)$ is the mutual information, and $h(\cdot)$ is the Shannon entropy, right? Also, what are $X$, $Y$ and $Z$? Apr4 revised Weak star limit language and notation Apr4 comment Weak star limit Sorry, I do not understand your question: what is $k$ in your definition? You defined $A^\epsilon$, what is $A_n$? (Is this homework?) Apr4 suggested approved edit on Weak star limit Apr3 comment Exercise Functional Analysis Also, you should really have a look at en.wikipedia.org/wiki/Derivation_(abstract_algebra) Apr3 awarded Commentator Apr3 comment Exercise Functional Analysis It seems to me that if you define an arbitrary value for $\mathcal O(x)$, then you can extend the operator uniquely to polynomials (and then by density to differentiable functions). Oct20 comment Positivity of the anti-commutator of two positive operators implies commutativity? Yes, indeed. The reason I was expecting them to commute is that if we call $P_B$ the ortogonal projector onto the kernel of $B$, then the fact that $\{ A, B \} \ge 0$ do imply that $A$ commutes with $P_B$. (in your example, this is trivial, but is not in general) Oct19 comment Positivity of the anti-commutator of two positive operators implies commutativity? Nice! I was pretty convinced that it was true. Oct19 accepted Positivity of the anti-commutator of two positive operators implies commutativity? Oct19 revised Positivity of the anti-commutator of two positive operators implies commutativity? just reformulating in proper English Oct19 comment Positivity of the anti-commutator of two positive operators implies commutativity? In your examples $A$ and $B$ are not Hermitian, and thus not positive, at least under one definition of positivity. Which is probably the most common. Where you thinking of the generalization of positivity for non hermitian matrices? Oct19 asked Positivity of the anti-commutator of two positive operators implies commutativity? Apr23 accepted Laplace transform with (real) compact support Apr18 asked Laplace transform with (real) compact support Aug30 comment Functional from $(0,+\infty)$ to $L^p(\mathbb R)$ It's ok: it was probably the only possible interpretation, and in fact looks like nobody misunderstood what you meant. Aug29 comment Functional from $(0,+\infty)$ to $L^p(\mathbb R)$ I am trying to understand how $f^r$ is defined: maybe you wanted to say that for every $r \in (0, \infty)$, $f^r$ is in $L^p(\mathbb{R})$. That's different from saying that for every $r$ we have $f^r : (0,\infty) \to L^p(\mathbb{R})$. Aug26 accepted Positive functionals on $\ell^\infty$ Aug24 revised Positive functionals on $\ell^\infty$ feel free to use AC Aug24 comment Positive functionals on $\ell^\infty$ I had looked for questions about "positive operator", but I forgot to look for "non-negative operators"... anyway, I'm perfectly fine with using AC, and I fact I edited my question adding the Banach limits as another class of positive operators. Thank you for the links!