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RAZVOJ ALGEBRE U INDIJI DO XVI VEKA

Pivarski, Dalibor (Beograd , 2025)

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URI: http://hdl.handle.net/123456789/5770

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v1_masterDaliborPivarski.pdf ( 1.742Mb )
KOHOMOLOGIJA GRUPA OSNOVNI POJMOVI I PRIMERI

Šon Kolins, Aleksandar (B , 2025)

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URI: http://hdl.handle.net/123456789/5769

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v1_masterAleksandarKolins.pdf ( 1.523Mb )

SLABA INTEGRACIJA VEKTOR-VREDNOSNIH FUNKCIJA SA VREDNOSTIMA U IDEALIMA OPERATORA I VEZA SA ELEMENTARNIM OPERATORIMA

Milović, Matija (Beograd , 2025)

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Abstract:

The subject of this dissertation is the study of the belonging of weak operator in- tegrals in appropriate ideals of compact operators, as well as the investigation of perturbation inequalities. These questions were previously considered in [16], where Cauchy–Schwarz type inequalities were established. In addition to providing norm estimates, these inequalities also yield sufficient conditions for an operator integral to belong to a given ideal. In the first part of the dissertation, using these inequalities, perturbation norm inequalities are derived for elementary operators generated by analytic functions. Specially, for an analytic function f, trigonometric polynomials T, S : R → C and t ∈ R, if fT S,t, f¯T T,t and f¯SS,t are the associated analytic functions, and if X ∈ B(H) and the operator P∞ n=1(AnXBn − CnXDn) belongs to a symmetric norming (s.n.) ideal CΦ(H), for some s.n. function Φ, then the following inequality holds ∞X n=1 (A∗ nAn− C∗ nCn) 1 2 fT S,t ∞X n=1 An⊗Bn X − fT S,t ∞X n=1 Cn⊗Dn X ∞X n=1 (BnB∗ n − DnD∗ n) 1 2 Φ ⩽ f¯T T,t ∞X n=1 A∗ nAn − f¯T T,t ∞X n=1 C∗ nCn 1 2 ∞X n=1 (AnXBn − CnXDn) × f¯SS,t ∞X n=1 BnB∗ n − f¯SS,t ∞X n=1 DnD∗ n 1 2 Φ , under certain conditions on the families (An)∞ n=1, (Bn)∞ n=1, (Cn)∞ n=1 and (Dn)∞ n=1 in B(H). Next, the dissertation considers vector measures induced by weak∗ integrable operator- valued functions taking values in Shatten–von Neumann ideals. Furthermore, the criteria for the compactness and nuclearity of the Gel’fand integral are derived, with emphasis on positive operator-valued functions. Finally, depending on the properties of the symmetric norming function Φ, the conse- quences of the condition sup e,f ∈B Z Ω Φ((⟨Aten, fn⟩)∞ n=1)dμ(t) < +∞. are explored. More precisely, it is proved that the weak∗ integral belongs to the symmetric ideal CΦ(H), as well as the Gelfand and Pettis integrability of the CΦ(H)-valued function A .

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http://hdl.handle.net/123456789/5768

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Matija_Milovic_doktorska_disertacija.pdf ( 2.652Mb )

MEHANIKA I STATIKA

Rašković, Danilo (Naučna Knjiga, Beograd , 1978)

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URI: http://hdl.handle.net/123456789/5767

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Mehanika_1_Stat ... 978_XI_Optimized-part1.pdf ( 8.656Mb )

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