ALL WE CAN NEVER BE

B(ℓ p ) can never be amenable

We show that, if E is a Banach space with a basis satisfying a certain condition, then the Banach algebra l∞(K(l2 ⊕ E)) is not amenable; in particular, this is true for E = l with p ∈ (1,∞). As a consequence, l∞(K(E)) is not amenable for any infinite-dimensional Lp-space. This, in turn, entails the non-amenability of B(lp(E)) for any Lp-space E, so that, in particular, B(lp) and B(Lp[0, 1]) are...

Should we all be vegetarians?

Can We Be Too Careful?

Good science? We should all be asking

Objectivity is a central tenet of the scientific process. That is, in order for science to be a successful tool for understanding the nature of reality it must be free from bias. This idea is so core to science that cases of explicit bias (e.g., data fabrication and false reporting of results) are both mystifying and sensational. In principle and (we hope) in practice, instances of bias can be ...

The Circle That Never Ends: Can Complexity Be Made Simple?

There is no need to try to ease into the discussion because the issue being discussed here is too involved to waste words that way. It is important to get right to the point. The starting premise is that we seek to understand the world in which we live. This leads immediately to a whole set of related premises that define the problem as being the answer to the question “how we can obtain that w...