Abstract:
We considerd and proved with an estimation the analogues of Brown-
Halmos and Neahri's theorems on the norms of Hankel operators,
acting on Subspaces of Hardy type reflexive rearrangement-invariant
spaces with nontrivial indices.
We studied invariant subspaces of the Bergman spaces on bounded
symmetric domains and quasi-invariant subspaces of the Segal-
Bergmann spaces. We completely characterized small Hankel
operators with finite rank on their spaces and showed a general result
of the degree. We showed the conditions that the product of two
Hankel operators is also a Hankel operator.
We derived new necessary and sufficient conditions for admissibility
observation operators for certain Co-semigroups.We also showed a
new sufficient criterion for admissibility for observation operators
with infinite-dimensional out-put space on contraction semigroups.
We found a sharp estimate of an infinite-time admissible observation
operator that leads to convergent of a normed of power
infinitesimal generator.