MERE NEKOMPAKTNOSTI NA HILBERTOVIM S*-MODULIMA

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MERE NEKOMPAKTNOSTI NA HILBERTOVIM S*-MODULIMA

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dc.contributor.advisor Kečkić, Dragoljub
dc.contributor.author Lazović, Zlatko
dc.date.accessioned 2019-12-23T17:32:19Z
dc.date.available 2019-12-23T17:32:19Z
dc.date.issued 2019
dc.identifier.uri http://hdl.handle.net/123456789/4819
dc.description.abstract In the first section we present the theory on uniform spaces and measures of noncompactness in metric and uniform spaces. Next, we recall the basic concepts and properties of C∗ and W∗-algebras and Hilbert modules over these algebras with some known topologies on Hilbert W∗-module. In the second section we construct a local convex topology on the standard Hilbert module l2(A), such that any compact” operator (i.e., any operator in the norm closure of the linear span of the operators of the form maps bounded sets into totally bounded sets. In the biginning A presents unital W∗-algebra, leter on A presents unital C∗-algebra. The converse is true in the special case where A = B(H) is the full algebra of all bounded linear operators on a Hilbert space H. In the third section we define a measure of noncompactness λ on the standard Hilbert C∗-module l2(A) over a unital C∗-algebra, such that λ(E) = 0 if and only if E is A-precompact (i.e. it is ε-close to a finitely generated projective submodule for any ε > 0) and derive its properties. Further, we consider the known, Kuratowski, Hausdorff and Istratescu measure of noncompactnes on l2(A) regarded as a locally convex space with respect to a suitable topology. We obtain their properties as well as some relationships between them and above introduced measure of noncompactness. In the forth section we generalize the notion of a Fredholm operator to an arbitrary C∗-algebra. Namely, we define finite type elements in an axiomatic way, and also we define a Fredholm type element a as such an element of a given C∗-algebra for which there are finite type elements p and q such that (1−q)a(1−p) is invertible. We derive an index theorem for such operators. In subsection Corollaries we show that many well-known operators are special cases of our theory. Those include: classical Fredholm operators on a Hilbert space, Fredholm operators in the sense of Breuer, Atiyah and Singer on a properly infinite von Neumann algebra, and Fredholm operators on Hilbert C∗-modules over a unital C∗-algebra in the sense of Mishchenko and Fomenko. en_US
dc.description.provenance Submitted by Slavisha Milisavljevic (slavisha) on 2019-12-23T17:32:19Z No. of bitstreams: 1 dr_Zlatko_Lazovic.pdf: 2019749 bytes, checksum: b94f99ebedc535ce3aa67ba5c432ae7a (MD5) en
dc.description.provenance Made available in DSpace on 2019-12-23T17:32:19Z (GMT). No. of bitstreams: 1 dr_Zlatko_Lazovic.pdf: 2019749 bytes, checksum: b94f99ebedc535ce3aa67ba5c432ae7a (MD5) Previous issue date: 2019 en
dc.language.iso sr en_US
dc.publisher Beograd en_US
dc.title MERE NEKOMPAKTNOSTI NA HILBERTOVIM S*-MODULIMA en_US
mf.author.birth-date 1977-10-17
mf.author.birth-place Novi Pazar en_US
mf.author.birth-country Srbija en_US
mf.author.residence-state Srbija en_US
mf.author.citizenship Srpsko en_US
mf.author.nationality Srbin en_US
mf.subject.area Mathematics en_US
mf.subject.keywords Uniform spaces, measures of noncompactness, Fredholm operators, C∗ and W∗-algebra, Hilbert modules, compact operators en_US
mf.subject.subarea Mathematical analysis en_US
mf.contributor.committee Arsenović, Miloš
mf.contributor.committee Krtinić, Djordje
mf.contributor.committee Arandjelović, Ivan
mf.university.faculty Mathematical faculty en_US
mf.document.references 67 en_US
mf.document.pages 135 en_US
mf.document.location Beograd en_US
mf.document.genealogy-project No en_US
mf.university Belgrade University en_US

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