ON CHARACTERIZATION OF POSINORMAL OPERATORS AND THEIR APPLICATIONS IN QUANTUM MECHANICS

Author's Name: JOHN P. AKELLO, C. RWENYO SABASI OMAORO, P. O. MOGOTU, and N. B. OKELO
Subject Area: Science and Engineering
Subject Mathematics
Section Research Paper

Keyword:

Hilbert space, Posinormal operators, Selfadjoint, norm inequality, Applications and Quantum Mechanics.


Abstract

Studies on Hilbert space operators have been carried out by several researchers and mathematicians with interesting results obtained. A posinormal operator is one of the operators under concern with interesting characters. Properties of posinormal operators have not been exhausted hence this calls for intense characterization of these operators. Of great concern is the norm inequality involving these operators. In this paper, we give a detailed study of the norm property of posinormal operators when they are sefadjoint. The objectives of the study are to: establish norm inequalities for posinormal operators; characterize posinormal operators and; determine applications of posinormal operators in other fields. The methodology involved the use of tensor products as a technical approach in determining these norm inequalities. The results show that the norm of a posinormal operator is equal to the norm of any normal operator when the operators are selfadjoint. The results obtained are very important in the classification of Hilbert space operators and their applications in other fields like quantum theory.

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