I have the following questions about dual norms : How do you prove that the dual of the dual norm is in fact the original norm? This is what I have so far: If I have $||y||_* $ as the norm dual of ...
Let $A$ be an $m\times n$-matrix and $B$ an $n \times m$-matrix over the same field. Consider the matrices $C=AB$ and $D=BA$. It is probably well known (and not difficult to show) that the only ...
Is the non-triviality of the algebraic dual of an infinite-dimensional vector space equivalent to the axiom of choice?
If $V$ is given to be a vector space that is not finite-dimensional, it doesn't seem to be possible to exhibit an explicit non-zero linear functional on $V$ without further information about $V$. The ...
Background I would like to know if there is some slick machinery to solve the following representation-theoretic problem. Let $\left(V,\langle-,-\rangle\right)$ be a finite-dimensional real inner ...
Hi there, Please tell me if I should divide these into individual questions next time. Short intro: Spherical Harmonics are a nice collection of functions. They are orthogonal and allow you to take ...
Consider a connected symplectic manifold $(M, \omega)$ of dimension $m=2n$. A few preliminary reminders (mostly to fix the notation): A vector field $X$ is symplectic if its flow preserves the ...
There is a nice tool in representation theory, the Howe duality, which as I know works for certain pairs of classical Lie algebras (the reference to the complete list of Howe dual pairs is appreciated ...