LEADER 01359nam 2200361 450 001 996280982203316 005 20231206213948.0 010 $a0-7381-6032-6 035 $a(CKB)3710000000578083 035 $a(NjHacI)993710000000578083 035 $a(EXLCZ)993710000000578083 100 $a20231206d2009 uy 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aISO/IEC/IEEE 9945:2009(E) $eInternational Standard - Information technology Portable Operating System Interface (POSIX)Base Specifications, Issue 7 /$fInstitute of Electrical and Electronics Engineers 210 1$aNew York :$cIEEE,$d2009. 215 $a1 online resource (85 pages) 517 $a9945-2009 - IEEE/ISO/IEC International Standard - Information technology Portable Operating System Interface 517 $a9945-2009 - International Standard - Information technology Portable Operating System Interface 517 $aInternational Standard - Information technology Portable Operating System Interface 517 $aISO/IEC/IEEE 9945 606 $aInformation technology 615 0$aInformation technology. 676 $a004 801 0$bNjHacI 801 1$bNjHacl 906 $aDOCUMENT 912 $a996280982203316 996 $aISO$91086301 997 $aUNISA LEADER 04183nam 2200565 a 450 001 9910438146103321 005 20251116201556.0 010 $a1-283-90829-8 010 $a3-0348-0478-4 024 7 $a10.1007/978-3-0348-0478-3 035 $a(CKB)2670000000279833 035 $a(EBL)1082166 035 $a(OCoLC)820329421 035 $a(SSID)ssj0000798659 035 $a(PQKBManifestationID)11459991 035 $a(PQKBTitleCode)TC0000798659 035 $a(PQKBWorkID)10743914 035 $a(PQKB)10681370 035 $a(DE-He213)978-3-0348-0478-3 035 $a(MiAaPQ)EBC1082166 035 $a(PPN)168307316 035 $a(EXLCZ)992670000000279833 100 $a20121003d2013 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aFunctional analysis in asymmetric normed spaces /$fStefan Cobzas 205 $a1st ed. 2013. 210 $aNew York $cSpringer$d2013 215 $a1 online resource (228 p.) 225 0$aFrontiers in mathematics,$x1660-8046 300 $aDescription based upon print version of record. 311 08$a3-0348-0477-6 320 $aIncludes bibliographical references and index. 327 $aIntroduction.- 1. Quasi-metric and Quasi-uniform Spaces. 1.1. Topological properties of quasi-metric and quasi-uniform spaces -- 1.2. Completeness and compactness in quasi-metric and quasi-uniform spaces.- 2. Asymmetric Functional Analysis -- 2.1. Continuous linear operators between asymmetric normed spaces -- 2.2. Hahn-Banach type theorems and the separation of convex sets -- 2.3. The fundamental principles -- 2.4. Weak topologies -- 2.5. Applications to best approximation -- 2.6. Spaces of semi-Lipschitz functions -- Bibliography -- Index. 330 $aAn asymmetric norm is a positive definite sublinear functional p on a real vector space X. The topology generated by the asymmetric norm p is translation invariant so that the addition is continuous, but the asymmetry of the norm implies that the multiplication by scalars is continuous only when restricted to non-negative entries in the first argument. The asymmetric dual of X, meaning the set of all real-valued upper semi-continuous linear functionals on X, is merely a convex cone in the vector space of all linear functionals on X. In spite of these differences, many results from classical functional analysis have their counterparts in the asymmetric case, by taking care of the interplay between the asymmetric norm p and its conjugate. Among the positive results one can mention: Hahn?Banach type theorems and separation results for convex sets, Krein?Milman type theorems, analogs of the fundamental principles ? open mapping, closed graph and uniform boundedness theorems ? an analog of the Schauder?s theorem on the compactness of the conjugate mapping. Applications are given to best approximation problems and, as relevant examples, one considers normed lattices equipped with asymmetric norms and spaces of semi-Lipschitz functions on quasi-metric spaces. Since the basic topological tools come from quasi-metric spaces and quasi-uniform spaces, the first chapter of the book contains a detailed presentation of some basic results from the theory of these spaces. The focus is on results which are most used in functional analysis ? completeness, compactness and Baire category ? which drastically differ from those in metric or uniform spaces.  The book is fairly self-contained, the prerequisites being the acquaintance with the basic results in topology and functional analysis, so it may be used for an introduction to the subject. Since new results, in the focus of current research, are also included, researchers in the area can use it as a reference text. 410 0$aFrontiers in Mathematics,$x1660-8046 606 $aFunctional analysis 615 0$aFunctional analysis. 676 $a515.7 700 $aCobzas?$b S?tefan$0769117 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910438146103321 996 $aFunctional Analysis in Asymmetric Normed Spaces$92541883 997 $aUNINA