β-operator in Banach Spaces

Abstract

To study some geometric properties of Banach space operator，the definitions of the β-operator and weak β-operator were given，and the properties of the β-operator and weak β-operator were discussed. Sufficient and necessary conditions for the operator with β-property were obtained. The relationship between properties of βoperator and the space which has β-property were discussed. The definition of β-operator space and the property of this space were studied. The conclusion was obtained that β-operator is a compact operator，and a new feature of reflexive space was given.

Keywords

• β-operator
• reflexive space
• weak β-operator
• β-operator space