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University of North Texas

1. Abbott, Catherine Ann. Operators on Continuous Function Spaces and Weak Precompactness.

Degree: 1988, University of North Texas

If T:C(H,X) – >Y is a bounded linear operator then there exists a unique weakly regular finitely additive set function m: – >L(X,Y**) so that T(f) = ∫Hfdm. In this paper, bounded linear operators on C(H,X) are studied in terms the measure given by this representation theorem. The first chapter provides a brief history of representation theorems of these classes of operators. In the second chapter the represenation theorem used in the remainder of the paper is presented. If T is a weakly compact operator on C(H,X) with representing measure m, then m(A) is a weakly compact operator for every Borel set A. Furthermore, m is strongly bounded. Analogous statements may be made for many interesting classes of operators. In chapter III, two classes of operators, weakly precompact and QSP, are studied. Examples are provided to show that if T is weakly precompact (QSP) then m(A) need not be weakly precompact (QSP), for every Borel set A. In addition, it will be shown that weakly precompact and GSP operators need not have strongly bounded representing measures. Sufficient conditions are provided which guarantee that a weakly precompact (QSP) operator has weakly precompact (QSP) values. A sufficient condition for a weakly precomact operator to be strongly bounded is given. In chapter IV, weakly precompact subsets of L1(μ,X) are examined. For a Banach space X whose dual has the Radon-Nikodym property, it is shown that the weakly precompact subsets of L1(μ,X) are exactly the uniformly integrable subsets of L1(μ,X). Furthermore, it is shown that this characterization does not hold in Banach spaces X for which X* does not have the weak Radon-Nikodym property. Advisors/Committee Members: Lewis, Paul Weldon, Bilyeu, Russell Gene, Appling, William D. L., Kung, Joseph P. S..

Subjects/Keywords: bounded linear operators; continuous function spaces; Riesz Representation Theorem; mathematics; Compact operators.; Functions, Continuous.

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Abbott, C. A. (1988). Operators on Continuous Function Spaces and Weak Precompactness. (Thesis). University of North Texas. Retrieved from https://digital.library.unt.edu/ark:/67531/metadc331171/

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16th Edition):

Abbott, Catherine Ann. “Operators on Continuous Function Spaces and Weak Precompactness.” 1988. Thesis, University of North Texas. Accessed August 13, 2020. https://digital.library.unt.edu/ark:/67531/metadc331171/.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7th Edition):

Abbott, Catherine Ann. “Operators on Continuous Function Spaces and Weak Precompactness.” 1988. Web. 13 Aug 2020.

Vancouver:

Abbott CA. Operators on Continuous Function Spaces and Weak Precompactness. [Internet] [Thesis]. University of North Texas; 1988. [cited 2020 Aug 13]. Available from: https://digital.library.unt.edu/ark:/67531/metadc331171/.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Abbott CA. Operators on Continuous Function Spaces and Weak Precompactness. [Thesis]. University of North Texas; 1988. Available from: https://digital.library.unt.edu/ark:/67531/metadc331171/

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

2. Širovnik, Nejc. Odvajanja in sorodne preslikave na nekaterih strukturah algebre in funkcionalne analize.

Degree: 2014, Univerza v Mariboru

Disertacija je sestavljena iz štirih delov. V prvem definiramo osnovne pojme, kot so prakolobar, polprakolobar in standardna operatorska algebra ter dokažemo znan rezultat, da je standardna operatorska algebra prakolobar. Nato spoznamo pojme klasični kolobar kvocientov, levi (desni, simetrični) Martindaleov kolobar kvocientov ter razširjen centroid, ki izhajajo iz teorije Martindaleovih kolobarjev kvocientov. Sledi vpeljava preslikav, kot so odvajanje, jordansko odvajanje, jordansko trojno odvajanje, posplošeno odvajanje, levi (desni) centralizator in levi (desni) jordanski centralizator ter predstavitev pomembnih rezultatov v zvezi z njimi. Prvi odmevnejši izrek tega področja sega v leto 1957, ko je Herstein dokazal, da je vsako jordansko odvajanje na prakolobarju brez elementov reda dva odvajanje. Njegov rezultat je leta 1975 na polprakolobarje brez elementov reda dva posplošil Cusack. M. Brešar je leta 1989 dokazal, da je vsako jordansko trojno odvajanje na polprakolobarju brez elementov reda dva odvajanje. Zalar je leta 1991 dokazal, da je vsak levi (desni) jordanski centralizator na polprakolobarju brez elementov reda dva levi (desni) centralizator. Chernoff je leta 1973 karakteriziral vsa linearna odvajanja na standardnih operatorskih algebrah. Na koncu prvega poglavja predstavimo še teorijo funkcijskih identitet (Brešar - Beidar - Chebotarjeva teorija), ki jo uporabimo pri rezultatih na prakolobarjih. V nadaljevanju predstavimo preslikave, ki zadoščajo določenim enakostim na standardnih operatorskih algebrah, prakolobarjih ter polprakolobarjih. V drugem poglavju obravnavamo aditivne preslikave v zvezi z odvajanji in jordanskimi odvajanji. Na standardnih operatorskih algebrah dokažemo vrsto rezultatov, ki motivacijo črpajo iz rezultatov in domnev Vukmana, Eremite in Kosi-Ulblove. S pomočjo teorije funkcijskih identitet na prakolobarjih dokažemo izrek, ki izhaja iz Vukmanove domneve. Sledi obravnava preslikav z določenimi lastnostmi na polprakolobarjih, ki ponekod vsebujejo enoto. Tretje poglavje posvetimo preslikavam, ki so povezane s centralizatorji. Predstavimo motivacijo za obravnavo dveh izrekov na standardnih operatorskih algebrah kompleksnega Hilbertovega prostora. V zadnjem poglavju se lotimo odvajanjem sorodnih preslikav na standardnih operatorskih algebrah, prakolobarjih in polprakolobarjih z enoto. Navdih za študij preslikav te vrste predstavljajo rezultati, ki jih predstavimo v prvem in drugem poglavju ter enakost, ki sta jo leta 2011 objavila M. Fošner in Vukman.

The dissertation consists of four parts. The first part introduces prime rings, semiprime rings and standard operator algebras. We present the proof of a known result, which states that every standard operator algebra is a prime ring. Later we define the terms classical ring of quotients, left (right, symmetrical) Martindale ring of quotients and extended centroid of a ring, which originate from the theory of Martindale rings of quotients. Afterwards follows an introduction of some specific additive mappings, such as…

Advisors/Committee Members: Vukman, Joso.

Subjects/Keywords: prakolobar polprakolobar; Banachov prostor; algebra omejenih linearnih operatorjev; standardna operatorska algebra; aditivna preslikava; odvajanje; jordansko odvajanje; jordansko trojno odvajanje; centralizator; involucija; funkcijska identiteta; omejen linearen operator.; prime ring; semiprime ring; Banach space; algebra of bounded linear operators; standard operator algebra; additive mapping; derivation; Jordan derivation; Jordan triple derivation; centralizer; involution; functional identity; bounded linear operator.; info:eu-repo/classification/udc/512.552(043.3)

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Širovnik, N. (2014). Odvajanja in sorodne preslikave na nekaterih strukturah algebre in funkcionalne analize. (Doctoral Dissertation). Univerza v Mariboru. Retrieved from https://dk.um.si/IzpisGradiva.php?id=44028 ; https://dk.um.si/Dokument.php?id=63352&dn= ; https://plus.si.cobiss.net/opac7/bib/20527112?lang=sl

Chicago Manual of Style (16th Edition):

Širovnik, Nejc. “Odvajanja in sorodne preslikave na nekaterih strukturah algebre in funkcionalne analize.” 2014. Doctoral Dissertation, Univerza v Mariboru. Accessed August 13, 2020. https://dk.um.si/IzpisGradiva.php?id=44028 ; https://dk.um.si/Dokument.php?id=63352&dn= ; https://plus.si.cobiss.net/opac7/bib/20527112?lang=sl.

MLA Handbook (7th Edition):

Širovnik, Nejc. “Odvajanja in sorodne preslikave na nekaterih strukturah algebre in funkcionalne analize.” 2014. Web. 13 Aug 2020.

Vancouver:

Širovnik N. Odvajanja in sorodne preslikave na nekaterih strukturah algebre in funkcionalne analize. [Internet] [Doctoral dissertation]. Univerza v Mariboru; 2014. [cited 2020 Aug 13]. Available from: https://dk.um.si/IzpisGradiva.php?id=44028 ; https://dk.um.si/Dokument.php?id=63352&dn= ; https://plus.si.cobiss.net/opac7/bib/20527112?lang=sl.

Council of Science Editors:

Širovnik N. Odvajanja in sorodne preslikave na nekaterih strukturah algebre in funkcionalne analize. [Doctoral Dissertation]. Univerza v Mariboru; 2014. Available from: https://dk.um.si/IzpisGradiva.php?id=44028 ; https://dk.um.si/Dokument.php?id=63352&dn= ; https://plus.si.cobiss.net/opac7/bib/20527112?lang=sl

3. Hernandez, Michelle Fernanda Pierri. Funções s-assintoticamente periódicas em espaços de Banach e aplicações à equações diferenciais funcionais.

Degree: PhD, Matemática, 2009, University of São Paulo

Este trabalho está voltado para o estudo de uma classe de funções contínuas e limitadas f : [0; \'INFINITO\') \'SETAX́ para as quais existe \'omega\́'> OU = ́0 tal que \'lim IND. t\́'SETA\́'INFINITO(́f(t + \'omega\') - f(t)) = 0. No decorrer do trabalho, chamaremos estas funções de S-assintoticamente \'omega\'-periódicas. Nós discutiremos propriedades qualitativas para estas funções e algumas relações entre este tipo de funções e a classe de funções assintoticamente \'omega\'-periódicas. Também estudaremos a existência de soluções fracas S-assintoticamente \'omega\'-periódicas para uma classe de primeira ordem de um problema de Cauchy abstrato bem como para algumas classes de equações diferenciais funcionais parciais neutras com retardo não limitado. Algumas aplicações para equações diferenciais parciais serão consideradas

This work is devoted to the study of the class of continuous and bounded functions f : [0 \'INFINIT\') \'ARROWX́ for which there exists \'omega&́#62; 0 such that \'limt IND.t \'ARROW\́'INFINIT\'(f(t + \'omega\'!) - f(t)) = 0 (in the sequel called S-asymptotically !-periodic functions). We discuss qualitative properties and establish some relationships between this type of functions and the class of asymptotically \'omega\'-periodic functions. We also study the existence of S-asymptotically \'omega\'-periodic mild solutions for a first-order abstract Cauchy problem in Banach spaces and for some classes of abstract neutral functional differential equations with infinite delay. Furthermore, applications to partial differential equations are given

Advisors/Committee Members: Táboas, Plácido Zoega.

Subjects/Keywords: Abstract Cauchy problem; Asymptoticallly almost periodic functions; Asymptotically periodic functions; Funções assintoticamente periódicas; Funções assintoticamente quase periódicas; Funções s-assintoticamente periódicas; Problema de Cauchy abstrato; S-asymptoticallly periodic functions; Semigroups of bounded linear operators; Semigrupos de operadores lineares limitados

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Hernandez, M. F. P. (2009). Funções s-assintoticamente periódicas em espaços de Banach e aplicações à equações diferenciais funcionais. (Doctoral Dissertation). University of São Paulo. Retrieved from http://www.teses.usp.br/teses/disponiveis/55/55135/tde-19052009-161255/ ;

Chicago Manual of Style (16th Edition):

Hernandez, Michelle Fernanda Pierri. “Funções s-assintoticamente periódicas em espaços de Banach e aplicações à equações diferenciais funcionais.” 2009. Doctoral Dissertation, University of São Paulo. Accessed August 13, 2020. http://www.teses.usp.br/teses/disponiveis/55/55135/tde-19052009-161255/ ;.

MLA Handbook (7th Edition):

Hernandez, Michelle Fernanda Pierri. “Funções s-assintoticamente periódicas em espaços de Banach e aplicações à equações diferenciais funcionais.” 2009. Web. 13 Aug 2020.

Vancouver:

Hernandez MFP. Funções s-assintoticamente periódicas em espaços de Banach e aplicações à equações diferenciais funcionais. [Internet] [Doctoral dissertation]. University of São Paulo; 2009. [cited 2020 Aug 13]. Available from: http://www.teses.usp.br/teses/disponiveis/55/55135/tde-19052009-161255/ ;.

Council of Science Editors:

Hernandez MFP. Funções s-assintoticamente periódicas em espaços de Banach e aplicações à equações diferenciais funcionais. [Doctoral Dissertation]. University of São Paulo; 2009. Available from: http://www.teses.usp.br/teses/disponiveis/55/55135/tde-19052009-161255/ ;

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