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bio website maths.leeds.ac.uk/~mdaws
location Leeds, UK
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Apr
15
revised What is “tilting” in the context of large deviations?
Removed backticks which were messing with the formatting
Apr
9
comment Adjoint operator of a Convex operator is convex
So that's an entirely different question... There is no obvious way to even form the adjoint when $A$ is not linear. Really you need to think about your application to get some inspiration as to what a suitable generalised definition might be...
Apr
9
comment Adjoint operator of a Convex operator is convex
What does that even mean? We always have that both sides are just equals.
Apr
9
comment Adjoint operator of a Convex operator is convex
But if $A$ if linear then $A(\lambda x_1+(1-\lambda)x_2) = \lambda A(x_1) + (1-\lambda)A(x_2)$ no inequality needed!
Apr
9
comment Adjoint operator of a Convex operator is convex
Yeah, I'm confused: if $A$ is linear then don't we just have equality, always, in your defining inequality? Or is $A$ not assumed linear in the 2nd part of the question? If so, then what's the definition of the adjoint?
Mar
29
awarded  Popular Question
Mar
6
comment Can we expect $\left\||f|^{2}f-|g|^{2}g\right\|\leq C ||f-g||$ in the Banach algebra $A(\mathbb T)$ ?
Although, I must say that the whole $M=2\|f_0\|$ thing is very mysterious...
Mar
6
comment Can we expect $\left\||f|^{2}f-|g|^{2}g\right\|\leq C ||f-g||$ in the Banach algebra $A(\mathbb T)$ ?
But that's not what the question asked: $f_0$ is fixed, this gives $M$ and then the OP specifically asks only for $f,g\in B_M$. If it was meant to be uniform, then why both with the $B_M$ condition?
Mar
6
answered Can we expect $\left\||f|^{2}f-|g|^{2}g\right\|\leq C ||f-g||$ in the Banach algebra $A(\mathbb T)$ ?
Mar
5
comment Does anybody know if the Fourier algebra of SL(3,Z) has an approximate identity?
What do you mean by "somewhat technical partial converse"? Just Thm 1.11, namely some sort of tensoring against a group with a sufficient rich set of representations?
Feb
13
awarded  Notable Question
Nov
20
comment How a unitary corepresentation of a Hopf C*-algebra, deals with the antipode?
Okay, I'm not sure I have much deeper to say than that actually...
Nov
20
comment How a unitary corepresentation of a Hopf C*-algebra, deals with the antipode?
Sure! But why the antipode behaves in this way is perhaps interesting (and, in some sense, forms the basis for the definition of the antipode in more complicated analytic quantum group settings).
Nov
19
comment How a unitary corepresentation of a Hopf C*-algebra, deals with the antipode?
Yes! Maybe look at Timmermann's book, "An invitation to quantum groups and duality.", as it's an good introduction, and nicely motivates from the analytic theory from algebraic considerations. But what you ask is true for general compact quantum groups.
Nov
18
comment Extending a $ * $-Representation of $ ({C_{c}}(G,\mathscr{A}),\star,^{*}) $ to a $ * $-Representation of $ \mathscr{A} \rtimes_{\alpha} G $
Well, I wouldn't accept! Let's hope someone comes along with some more thoughts (as I think this is a nice question!)
Nov
18
comment Extending a $ * $-Representation of $ ({C_{c}}(G,\mathscr{A}),\star,^{*}) $ to a $ * $-Representation of $ \mathscr{A} \rtimes_{\alpha} G $
So this is definitely not an answer... just a comment that was too long for a 2comment"...
Nov
18
comment Extending a $ * $-Representation of $ ({C_{c}}(G,\mathscr{A}),\star,^{*}) $ to a $ * $-Representation of $ \mathscr{A} \rtimes_{\alpha} G $
Yes... the point of my comment was that you cannot find such a counter-example for G discrete or compact. So I suggested you look at $\mathbb R$, this being an example I couldn't immediately see...
Nov
17
revised Extending a $ * $-Representation of $ ({C_{c}}(G,\mathscr{A}),\star,^{*}) $ to a $ * $-Representation of $ \mathscr{A} \rtimes_{\alpha} G $
added 557 characters in body
Nov
16
answered Extending a $ * $-Representation of $ ({C_{c}}(G,\mathscr{A}),\star,^{*}) $ to a $ * $-Representation of $ \mathscr{A} \rtimes_{\alpha} G $
Nov
16
comment Extending a $ * $-Representation of $ ({C_{c}}(G,\mathscr{A}),\star,^{*}) $ to a $ * $-Representation of $ \mathscr{A} \rtimes_{\alpha} G $
Btw, in your definition of the product, you need to replace $a\in A$ by a group element.