Ph.D Thesis | |

Ph.D Student | Helmer Leonid |
---|---|

Subject | Factorizations and Reflexivity in Non Commutative Hardy Algebras |

Department | Department of Mathematics |

Supervisor | PROFESSOR EMERITUS Baruch Solel |

Full Thesis text |

In 2004 P. Muhly and B. Solel
introduced the non commutative Hardy algebras *H ^{∞}*(

In the study of these non commutative
analogs, one would like to understand to what extent known properties *H ^{∞}* (D) can be generalized to properties of
these non commutative algebras.

In this thesis we view the algebra *H ^{∞}*(

We develop our version of the
inner-outer factorization starting with the factorization of a vector on the underlying Hilbert
space. We then construct the inner-outer factorization of an element of the commutant of our
algebra, which is the Hardy algebra of the dual correspondence. Finally, using the
duality of correspondences, we construct the factorization of an element of *ρ*(*H ^{∞}*(

Regarding reflexivity, we prove that every
operator in *Alg Lat ρ*(*H ^{∞}*(

Finally, we show also the reflexivity
of the compression of the Hardy algebra to a suitable coinvariant subspace **M**, which may be thought of as a generalized symmetric Fock
space.