Subnormality and Compactness Characterizations of Toeplitz Operators in Algebra of Fock Spaces

Abstract

We study subnormal and hyponormal Toeplitz operators with extremal problems of Hardy spaces. The compact Toeplitz operators by the Berezin transform on bounded symmetric domains, heat flow and bounded mean oscillation are shown. We determine which subnormal Toeplitz operators are either normal or analytic and the Kernels of their Self – Commutators. We obtain the gap between subnormality and hypnormality for block Toeplitz operators with spectra and quasinormal Toeplitz operators. The Toeplitz operators with bounded mean oscillation symbols on the Segal – Baragmann space, Fock space and compactness characterizations of operators in the Toeplitz algebra of the Fock space are discussed.