LEADER 03494nam 2200541 450 001 996466732703316 005 20211005195853.0 010 $a3-030-67417-7 024 7 $a10.1007/978-3-030-67417-5 035 $a(CKB)4100000011786542 035 $a(DE-He213)978-3-030-67417-5 035 $a(MiAaPQ)EBC6509604 035 $a(Au-PeEL)EBL6509604 035 $a(OCoLC)1241445668 035 $a(PPN)254722601 035 $a(EXLCZ)994100000011786542 100 $a20211005d2021 uy 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 12$aA primer on Hilbert space theory $elinear spaces, topological spaces, metric spaces, normed spaces, and topological groups /$fCarlo Alabiso, Ittay Weiss 205 $aSecond edition. 210 1$aCham, Switzerland :$cSpringer,$d[2021] 210 4$dİ2021 215 $a1 online resource (XXII, 328 p. 19 illus.) 225 1 $aUNITEXT for Physics,$x2198-7882 311 $a3-030-67416-9 327 $a1. Hilbert Space Theory - A Quick Overview -- 2. Linear Spaces -- 3. Topological Spaces -- 4. Metric Spaces -- 5. The Lebesgue Integral Following Mikusiniski -- 6. Banach Spaces -- 7. Hilbert Spaces -- 8. A Survery of mathematical structures related to Hilbert space theory -- 9. Solved Problems. 330 $aThis book offers an essential introduction to the theory of Hilbert space, a fundamental tool for non-relativistic quantum mechanics. Linear, topological, metric, and normed spaces are all addressed in detail, in a rigorous but reader-friendly fashion. The rationale for providing an introduction to the theory of Hilbert space, rather than a detailed study of Hilbert space theory itself, lies in the strenuous mathematics demands that even the simplest physical cases entail. Graduate courses in physics rarely offer enough time to cover the theory of Hilbert space and operators, as well as distribution theory, with sufficient mathematical rigor. Accordingly, compromises must be found between full rigor and the practical use of the instruments. Based on one of the authors?s lectures on functional analysis for graduate students in physics, the book will equip readers to approach Hilbert space and, subsequently, rigged Hilbert space, with a more practical attitude. It also includes a brief introduction to topological groups, and to other mathematical structures akin to Hilbert space. Exercises and solved problems accompany the main text, offering readers opportunities to deepen their understanding. The topics and their presentation have been chosen with the goal of quickly, yet rigorously and effectively, preparing readers for the intricacies of Hilbert space. Consequently, some topics, e.g., the Lebesgue integral, are treated in a somewhat unorthodox manner. The book is ideally suited for use in upper undergraduate and lower graduate courses, both in Physics and in Mathematics. 410 0$aUNITEXT for Physics,$x2198-7882 606 $aHilbert space 606 $aTopological spaces 606 $aMetric spaces 615 0$aHilbert space. 615 0$aTopological spaces. 615 0$aMetric spaces. 676 $a515.733 700 $aAlabiso$b Carlo$0521485 702 $aWeiss$b Ittay 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996466732703316 996 $aA primer on Hilbert space theory$91902336 997 $aUNISA