master's thesis
Selma Paljanin (Author), Roman Drnovšek (Mentor)

Abstract

We introduce some basic theory about numerical range and numerical radius. Basic inequalities for numerical radius which involve one operator and basic inequalities which involve product of two commutative operators are studied. We then introduce more complex numerical radius inequalities for one operator, finding some upper bounds for the nonnegative quantites $\|T\|-w(T)$ and $\|T\|^2-w^2(T)$ under different assumptions for operator $T$, including inequalities for some associated functionals. We establish new inequalities for composite operators generated by some operators $A$ and $B$ under certain assumptions on $A$ and $B$. We introduce a functional $\mu(A,B)$ associated with two operators and study upper bounds for nonnegative differences $\mu(A,B)-w(B^{\ast}A)$ and $\mu^2(A,B)-w^2(B^{\ast}A)$. Finally, we introduce Euclidean Operator Radius and extend some earlier results to Euclidean radius of two operators.

Keywords

mathematics;numerical range;numerical radius;reverse inequalities;associated functionals;Euclidean operator radius;

Data

Language: English
Year of publishing:
Typology: 2.09 - Master's Thesis
Organization: UL FMF - Faculty of Mathematics and Physics
Publisher: [S. Paljanin]
UDC: 517.983
COBISS: 101875715 Link will open in a new window
Views: 1060
Downloads: 60
Average score: 0 (0 votes)
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Other data

Secondary language: Slovenian
Secondary title: Neenakosti za numerični radij
Secondary abstract: Predstavili bomo osnove teorije o numeričnem zakladu in numeričnem radiju. Preučili bomo osnovne neenakosti numeričnega radija, ki vsebujejo en operator in osnovne neenakosti, ki vsebujejo produkt dveh komutativnih operatorjev. Nato bomo predstavili kompleksnejše neenakosti numeričnega radija za en operator, pri čemer bomo iskali zgornje meje nenegativnih količin $\|T\|-w(T)$ in $\|T\|^2-w^2(T)$ pod različnimi predpostavkami za operator $T$, vključno z neenakostmi nekaterih pridruženih funkcionalov. Zasnovali bomo nove neenakosti za sestavljene operatorje, ki jih generirata neka operatorja $A$ in $B$, pod določenimi predpostavkami za $A$ in $B$. Vpeljali bomo funkcional $\mu(A,B)$, ki je povezan z dvema operatorjema, in preučili zgornje meje za nenegativni razliki $\mu(A,B)-w(B^{\ast}A)$ ter $\mu^2(A,B)-w^2(B^{\ast}A)$. Na koncu bomo predstavili evklidski radij operatorja in nekatere rezultate od prej razširili na evklidski radij dveh operatorjev.
Secondary keywords: matematika;numerični zaklad;numerični radij;obratne neenakosti;pridruženi funkcionali;evklidski radij operatorja;
Type (COBISS): Master's thesis/paper
Study programme: 0
Embargo end date (OpenAIRE): 1970-01-01
Thesis comment: Univ. v Ljubljani, Fak. za matematiko in fiziko, Oddelek za matematiko, Matematika - 2. stopnja
Pages: XI, 61 str.
ID: 14785284