Generalized Operator Valued Integral

Background/Objectives: Hilbert space has been studied in previous researches more than a century. In1 introduced fusion integral as an operator valued integral over a Hilbert space. Methods/Statistical Analysis: A generalized operator valued integral over a Hilbert space is presented. Also we obtain results concerning composition a generalized operator valued integral with a bounded objective operator on Hilbert space. Findings: Theory and definitions are developed based on Generalized Operator Valued Integra and its findings include: 2000 Mathematics Subject Classification. Primary: 42C15; Secondary 46L30. The approaches and opinion of the operator valued integral case has validated and assisted to the operator approach. Applications/Improvements: One of the problems in the development of frame theory has been the using of an impressive structure for the subject, which is used in this paper.