Musundi Sammy Wabomba

• Professor
• Chuka University

The study of operators in Hilbert spaces is an important concept due to its wide application in areas like computer programming, financial mathematics and quantum physics. This paper focused on a class of square normal operators in a Hilbert space. Let H be a complex Hilbert space and B(H) be a bounded linear operator acting on H. Then an operator...

Fixed-point theory (FPT) has lot of applications not only in the field of mathematics but also in various other disciplines. Fixed Point Theorem presents that if T:X \(\to\) X is a contraction mapping on a complete metric space (X, d) then there exists a unique fixed point in X. FPT is also essential in game theory, in this case Brower Fixed Point...

Hypercyclicity criterion has been an important tool in the test of hypercyclicity of different operators. This tool has been used by different mathematicians to show that generalized derivations, left and right multiplication operators, operator algebra and backward shift operators are hypercyclic. In the current paper we show that a basic elementa...

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 propert...

The norm property of different types of Elementary operators has attracted a lot of researchers due to its wide range applications in functional analysis. From available literature the norm of Jordan elementary operator has been determined in C*-algebras, JB*-algebras, standard operator algebra and prime JB*-triple but not much has been done in ten...

Many researchers in operator theory have attempted to determine the relationship between the norm of an elementary operator of length two and the norms of its coefficient operators. Various results have been obtained using varied approaches. In this paper, we attempt this problem by the use of the Stampfli’s maximal numerical range in a tensor prod...

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. In this paper therefore, the study aims to det...

Application of Fixed-Point Theorem has tremendously increased in different areas of interest and research. Fixed Point Theorem presents that if T:X→X is a contraction mapping on a complete metric space (X, d) then there exists a unique fixed point in X. A lot has been done on application of contraction mapping in Fixed Point Theorem on metric space...

In this paper, we investigate some transitivity action properties of the cartesian product of the alternating group \(A_{n}(n \geq 5)\) acting on a cartesian product of ordered sets of triples using the Orbit-Stabilizer Theorem by showing that the length of the orbit \((p, s, v) \text { in } A_{n} \times A_{n} \times A_{n},(n \geq 5)\) acting on \(...

Operators in Hilbert space have properties which are useful in the study of mathematical abstract areas such as approximation theory, Banach Fixed point theory, the spectral theory as well as Quantum Mechanics. Schrödinger equation is a fundamental entity with many applications in Quantum Mechanics. This equation was initially derived by applying t...

A. Some researchers in combinatorics have developed permutation algorithms using different approaches. We contribute to this area by developing a formula for generating permutations whereby, starting with an identity permutation, each succeeding permutation is a composition on the preceding one. We also determine the conditions by which the resulti...

Some researchers in combinatorics have developed permutation algorithms using different approaches. We contribute to this area by developing a formula for generating permutations whereby, starting with an identity permutation, each succeeding permutation is a composition on the preceding one. We also determine the conditions by which the resulting...

Nitrogen is a vital nutrient that enhances plant growth which has motivated the intensive use of nitrogen-based fertilizers to boost crop productivity . However, Pollution by nitrate is a globally growing problem due to the population growth, increase in the demand for food and inappropriate Nitrogen application.The complexities and challenges in q...

The numerical range has been studied extensively in Hilbert spaces. Properties of the numerical range such as non-emptiness, containment of the spectrum and in particular, convexity have been proved and results have been given in these spaces. Furthermore, comparison of the numerical ranges with the spectra have been established. In this study, we...

Nitrogen is a vital nutrient that enhances plant growth which has motivated the intensive use of nitrogen based fertilizers to boost crop productivity. However, Pollution by nitrate is a globally growing problem due to the population growth, increase in the demand for food and inappropriate Nitrogen application. The complexities and challenges in q...

Properties of elementary operators have been studied over the past years especially the norm aspect. Various results have been obtained on elementary operators of different lengths using different approaches. In this paper, we determine the norm of an elementary operator of length n in a C*algebra using finite rank operators.We will review known re...

HIV/AIDS remains one of the leading causes of death in the world with its effects most devastating in Sub Saharan Africa due to its dual infection with opportunistic infections especially malaria and tuberculosis. This study presents a co infection deterministic model defined by a system of ordinary deferential equations for HIV/AIDS, malaria and t...

Various results that relate to almost similarity and other classes of operators such as isometry, normal, unitary and compact operators have been extensively discussed. It has been shown that if operators S and T are unitarily equivalent, then S is almost similar to T. Similarly, it has been shown that if operators A and B are such that A is almost...

The Gross Domestic Product (GDP) is the market value of all goods and services produced within the borders of a nation in a year. In this paper, Kenya's annual GDP data obtained from the Kenya National Bureau of statistics for the years 1960 to 2012 was studied. Gretl and SPSS 21 statistical softwares were used to build a class of ARIMA (autoregres...

This paper assesses the potential impact of commercialization of agriculture on household welfare of farmers in eastern Kenya under the Mwea rice scheme. The study consists of cross-sectional data collected with structured survey questionnaires, Stratified sampling was adopted with each of the four zones in the District forming a strata, 368 respon...

The real exchange rate has proven to be an important factor in international trade because it is expected that exports respond to real exchange rate movements with respect to the characteristics of the importing and exporting countries. Exchange rate volatility increases uncertainty of profits on contracts denominated in foreign currency and subseq...

In this paper we introduce the notion of Quasi-similarity of bounded linear operators in Hilbert Spaces. We do so by defining a quasi-affinity from one Hilbert Space H to K. Some results on quasi-affinities are also discussed. It has already been shown that on a finite dimensional Hilbert Space, quasi similarity is an equivalence relation that is;...

The Banach space operator ideals and nuclear maps have a large class of morphisms which behave as if they were part of a compact closed category, that is, they allow one to transfer variables between the domain and the codomain. We use the concept of nuclearity in functional analysis to establish application aspect of Banach space ideal properties...

We consider the almost similarity property which is a new class in operator theory and was first introduced by A. A. S. Jibril. We establish that almost similarity is an equivalence relation. Some results on almost similarity and isometries, compact operators, hermitian, normal and projection operator are also shown. By characterization of unitary...

Similarity and unitary equivalence can be shown to be of equivalence relations. We discuss a result showing that two similar operators have equal spectra (i.e. point and approximate point spectrum). More so, unitary equivalence results for invariant subspaces and normal operators are proved. For similar normal operators, we state the Fuglede – Putn...

Let X, Y be Banach spaces and consider the w'-topology (the dual weak operator topology) on the space (L(X, Y) of bounded linear operators from X into X with the uniform operator norm. L w' (X, Y) is the space of all T ∈ L(X, Y) for which there exists a sequence of compact linear operators (Tn) ⊂ K(X, Y) such that T = w' - lim nT n. Two equivalent...

Similarity and unitary equivalence can be shown to be of equivalence relations. We discuss a result showing that two similar operators have equal spectra (i.e. point and approximate point spectrum). More so, unitary equivalence results for invariant subspaces and normal operators are proved. For similar normal operators, we state the Fuglede – Putn...