Browsing by Author "Musundi Sammy Wabomba"

Filter results by typing the first few letters
Now showing 1 - 2 of 2
  • Thumbnail Image
    Item
    Properties of Isosceles, Pythagorean and Isosceles-Pythagorean Vectors in the Characterization of Hilbert Spaces
    (Asian Journal of Pure and Applied Mathematics, 2024-11-05) Damaris Njeri Mugure; Musundi Sammy Wabomba; Alice Lunani Murwayi
    All Hilbert spaces are Banach spaces but the converse is not necessarily true. Characterization of Banach spaces as Hilbert spaces has had different approaches for various Banach spaces. It has been shown that a separable Banach space which is almost transitive with vector orthogonalities for dimension greater than three is a Hilbert space. It worthy to note that micro transitivity together with Isosceles (I), Pythagorean (P) and Isosceles Pythagorean (IP) orthogonalities in the unit sphere have some essential properties that can be considered in characterization of Hilbert spaces. In this study, separable micro transitive Banach spaces are examined and their characterization as Hilbert spaces is achieved by applying the I-vector property in affine sets along with the P and IP-vector properties. In particular, by letting a separable Banach space 𝑋 of 𝑑𝑖𝑚𝑋 ≥ 2 possessing micro transitivity property with I, P, and IP vectors, then 𝑋 is a Hilbert space. The results of this research are expected to be useful in algebra and differential operators, particularly for calculating wave functions and formulation of theory
  • Thumbnail Image
    Item
    Properties of Unitary Quasi-Equivalence on Isometry, Co-Isometry, and Partial Isometry Operators
    (2024-04-16) Anyembe Lilian; Musundi Sammy Wabomba; Kinyanjui Jeremiah Ndung’u
    The present study aims to determine the properties of unitary quasi-equivalence and isometry, co-isometry and partial isometry operators. Unitary quasi- equivalence has been shown to be an equivalence relation. Similarly, unitary quasi-equivalence has been proven to preserve normality, hyponormality and binormality of operators. However, the properties of unitary quasi-equivalence and partial isometric operators have not been established. Based on the preceding results, it establishes that unitary quasi-equivalent operators preserve; isometry, co-isometry and partial isometric properties.