  In 1955 Kadison \cite{14} asked whether the analogue of the classical
Burnside's theorem of the Linear Algebra holds in the infinite dimensional
case. We use reproducing kernels method to solve the Kadison question. Namely,
we prove that any proper weakly closed subalgebra $\mathcal{A}$ of the algebra
$\mathcal{B}\left( H\right) $ of bounded linear operators on infinite
dimensional complex Hilbert spaces $H$ has a nontrivial invariant subspace,
i.e., $\mathcal{A}$ is a nontransitive algebra. This solves The Transitive
Algebra Problem positively, and hence Hyperinvariant Subspace Problem and
Invariant Subspace Problem are also solved positively. In this context, we also
consider the celebrated Riemann Hypothesis of the theory of meromorphic
functions and solve it in negative.
