On Some Properties of Quantum Stochastic Multivalued Operators

L. A.  Abimbola; E. O.  Ayoola

L. A. Abimbola Department of Mathematics and Statistics, Abiola Ajimobi Technical University, Ibadan, Oyo State, Nigeria.
E. O. Ayoola Department of Mathematics, University of Ibadan, Oyo State, Nigeria.

Keywords: Multivalued operators, Quantum stochastic operator, Quantum stochastic processes

Abstract

This paper explores the properties of multivalued maps associated with quantum stochastic operators as formulated by Hudson and Parthasarathy. We focus on key aspects including the measure of noncompactness, continuity of multivalued operators, and the condensing property. Also, we consider measurability, strong measurability, the Castaining representation, and the Lusin property. These findings contribute to a deeper understanding of the behavior of multivalued operators in quantum stochastic analysis and highlight the interconnectedness of these properties within the framework of quantum stochastic analysis. By investigating this properties, our work provides valuable insights that could inform future research and enhance the theoretical foundation of quantum stochastic processes.

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