Abstract
Hamiltonians, momentum operators, and other quantum-mechanical perceptible take the form of self-adjoint operators
when understood in quantized physical schemes. Unbounded and self-adjoint recognition are required in the situation
of positive measurements. The selection of the proper Hilbert space(s) and the selection of the self-adjoint extension
must be made in order for this to operate. In this effort, we define a new extension positive measure depending on the
measurable field of nonzero positive self-adjoint operator in unbounded Hilbert space of analytic functions of complex
variables. Consequently, we define an extension norm in the same space. We show several new properties of the suggested
operator and its adjoin operator. These properties include the posinormality, inclusion property, isolating property and
achieving the Weyl’s and Browder’s theorems.
when understood in quantized physical schemes. Unbounded and self-adjoint recognition are required in the situation
of positive measurements. The selection of the proper Hilbert space(s) and the selection of the self-adjoint extension
must be made in order for this to operate. In this effort, we define a new extension positive measure depending on the
measurable field of nonzero positive self-adjoint operator in unbounded Hilbert space of analytic functions of complex
variables. Consequently, we define an extension norm in the same space. We show several new properties of the suggested
operator and its adjoin operator. These properties include the posinormality, inclusion property, isolating property and
achieving the Weyl’s and Browder’s theorems.
Keywords
Browder’s theorem
Posinormality
Positive measurement
Self-adjoint operator
Unbounded Hilbert space
Unbounded operator
Weyl’s theorem