The class of D(T*) – operators on Hilbert spaces

Key Points

• The paper aims to introduce and explore the properties of D(T*)-operators on separable Hilbert spaces.
• Defined T as an operator on separable Hilbert space H.
• Established a condition for T to be a D(T*)-operator involving another operator U.
• Studied main properties of D(T*)-operators.
• Introduced a new class of operators characterized by the relation TT*U = UTT*.
• Outlined the fundamental properties and implications of D(T*)-operators.