  In these notes, we investigate the tail behaviour of the norm of subgaussian
vectors in a Hilbert space. The subgaussian variance proxy is given as a trace
class operator, allowing for a precise control of the moments along each
dimension of the space. This leads to useful extensions and analogues of known
Hoeffding-type inequalities and deviation bounds for positive random quadratic
forms. We give a straightforward application in terms of a variance bound for
the regularisation of statistical inverse problems.
