Vol. 8 No. 1 (2024): Vol 8, Iss 1, Year 2024
Articles

A study on the hilbert space structure and positive operators

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  • Raviraj R,
  • Mohamed Ali A
Raviraj R
Department of Mathematics, Akshara PU & Degree College, Anekal, Karnataka, India
Mohamed Ali A
Associate professor, Department of Mathematics, Islamiah College (Autonomous), Vaniyambadi – 635752, India
DOI: https://doi.org/10.26524/cm185
Published June 30, 2024
Keywords
  • Positive operator, Symmetric operator, Hilbert space characterization, Equivalent norm, Complemented subspace, Accretive operator.
How to Cite
Raviraj R, & A, M. A. (2024). A study on the hilbert space structure and positive operators. Journal of Computational Mathematica, 8(1), 038-041. https://doi.org/10.26524/cm185

Abstract

Let X be a real Banach space. We prove that the existence of an injective, positive, symmetric and not strictly operator from X into its dual implies that either X admits an equivalent Hilbertian norm or it contains a nontrivially complemented subspace which is isomorphic to a Hilbert space. We also treat the non-symmetric case.

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