Browsing by Author "Sakwa, Cyprian O."

Browsing by Author "Sakwa, Cyprian O."

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  • Certain Properties Involving the Joint Essential Numerical Ranges 
    Sakwa, Cyprian O. (2020)
    The concept of essential numerical range of an operator was dened and studied by Stamp i and Williams in 1972. Researchers generalised this idea of essential numerical range to a group of operators to the joint essential ...
  • Curvilinear co-ordinates and expression of motion equations from vector form to cylindrical co-ordinates 
    Sakwa, Cyprian O.; Masibayi, Andrew; Okelo, N. B. (Hindawi, 2015-05)
    In this paper, we consider at the equations of motion in vector form and convert them to cylindrical coordinates.We also consider the continuity and momentum properties of these equations.
  • Expression of motion equations from vector form to spherical coordinates 
    Masibayi, Andrew; Sakwa, Cyprian O.; Okelo, N. B. (Hindawi, 2015-05)
    Navier-Stokes equations are the equations of conservation of linear momentum.In this paper we express this type of equation from vector form to spherical co-ordinates. We refer to some equations in this paper ...
  • A note on the joint essential numerical range of aluthge transform 
    Sakwa, Cyprian O. (2018)
    Denote by T the bounded linear operator on a complex Hilbert space X and let T = U|T | be any polar decomposition of T with U a partial isometry and |T | = (T ∗T ) 1 2 . Then, the Aluthge transform Te of T is the operator ...
  • On Norms of Derivations Implemented by Self-Adjoint Operators 
    Shagwila, Victor; Okelo, N. B.; Obogi, Robert; Sakwa, Cyprian O. (2019-05)
    In the present paper, we introduce and study the concept of norms of derivations, in particular norm estimates of derivations implemented by self-adjoint operators. We show that kδC k = kCX −XCk ≤ 2kCk, for inner derivation ...
  • On relation between the joint essential spectrum and the joint essential numerical range of aluthge transform 
    Sakwa, Cyprian O. (2021-08-13)
    Associated with every commuting m-tuples of operators on a complex Hilbert space X is its Aluthge transform. In this paper we show that every commuting m-tuples of operators on a complex Hilbert space X and its Aluthge ...
  • On the convexity of the joint essential numerical ranges 
    Sakwa, Cyprian O.; Masibayi, Andrew; Okelo, N. B. (Hindawi, 2015-05)
    The concept of essential numerical range of an operator was defined and studied by Stampfli and Williams in 1972. In this paper, we consider the joint essential numerical range of an m-tuple of operators T = (푇1,...,푇푚)in ...
  • On the joint essential maximal numerical ranges 
    Sakwa, Cyprian O.; Masibayi, Andrew; Okelo, N. B. (Hindawi, 2015-05)
    The concept of maximal numerical range of a bounded operator T on B(X) was introduced and studied in by Stampfli who used it to derive an identity for the norm of derivation. This concept was later generalised by Ghan ...
  • Remarks on Essential Maximal Numerical Range of Aluthge Transform 
    Sakwa, Cyprian O.; Chikamai, L.; Aywa, S. (SciPress, 2019)
    This paper focuses on the properties of the essential maximal numerical range of Aluthge transform Te. For instance, among other results, we show that the essential maximal numerical range of Aluthge transform is nonempty ...
  • Results on the joint essential maximal numerical ranges 
    Sakwa, Cyprian O. (2020-05)
    In the present paper, we show the equivalent denitions of the joint essential maximal numerical range. In the current paper, we show that the properties of the classical numerical range such as compactness also hold for ...
  • Some properties of the joint numerical range of the aluthge transform 
    Sakwa, Cyprian O.; Aywa, S.; Chikamai, L. (2018)
    The study of the Aluthge transform Te was introduced and studied by Aluthge in his study of p-hyponormal operators in 1990. Several researchers have since studied various properties of the transform for a single operator ...
  • A Study on the Joint Maximal Numerical Range of Aluthge Transform 
    Sakwa, Cyprian O. (2018-08)
    The Aluthge transform Te of a bounded linear operator T on a complex Hilbert space X is the operator |T| 1 2 U|T| 1 2 . Here, T = U|T| is any polar decomposition of T with U a partial isometry and |T| = (T ∗T) 1 2 . This ...
  • A survey of folding-based zero-knowledge proofs 
    Sakwa, Cyprian O.; Anyembe, Andrew O.; Li, Fagen (Elsevier, 2026-01)
    This survey uniquely approaches zero-knowledge proofs (ZKPs) through the lens of folding schemes, offering a fresh framework to analyze efficiency, scalability, and post-quantum resilience. By focusing on folding, we unify ...

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