/sci/ - Science & Math

Consider the space of trace class (nuclear) operators [math]T(\mathcal{H})[/math] on a separable Hilbert space as the dual of the space of compact operators [math]K(\mathcal{H})[/math] on the Hilbert space.

Is the weak-* topology on [math]T(\mathcal{H})[/math] weaker or stronger than the weak operator topology (i.e. the topology induced by seminorms of the type [math]|\langle Tx,y\rangle|[/math] for [math]x,y \in \mathcal{H}[/math])?

What actually causes libido?
Why do some people have a high libido while others have a low one?

I've looked it up and it's always been somewhat inconclusive
>Inb4 it's something in your genes bro
Yeah but what do those genes manifest as? More of a certain neurotransmitter? Better blood flow? More testosterone? How do they affect you to create libido?

Question about American academia. Is "associate professor" always a tenured position in the US?

I've seen associate professors without tenure in Asia, that's why I'm curious.