Subdiagonal Subalgebras and Commutative Banach Algebras by Toeplitz Operators

Abstract

We determine the eigenvalues inequalities, sums of hermitian and normal matrices, Schubert calculus, Wielant’s theorem with spectral sets and Banach algebra. The principal submatrices with noncommutative function theory and unique extensions was shown. We give applications of the Fuglede-Kadison determinant, Riesz and Szego ̈ type factorizations theorem for noncommutative Hardy spaces and for a Helson-Szego ̈ theorem noncommutative Hardy-Lorentz spaces. We also give a Helson-Szego ̈ subdiagonal subalgebras with applications to Toeplitz operators. The algebraic structure of non-commutative analytic with quasi-radial quasi-homogeneous symbols and commutative Banach algebra of Toeplitz algebra and operators are presented, the structure of a commutative Banach algebra on the unit ball and quasi-nilpotent group action, generated by Toeplitz operators with quasi-radial quasi-homogeneous symbols are discussed.