000 03349nam a2200397Ki 4500
001 ocn861693022
003 OCoLC
005 20240726105433.0
008 131029s2011 enk ob 001 0 eng d
040 _aNT
_beng
_erda
_epn
_cNT
020 _a9780191548543
_q((electronic)l(electronic)ctronic)l((electronic)l(electronic)ctronic)ctronic bk.
050 0 4 _aQA322
_b.I587 2011
049 _aNTA
100 1 _aAllan, Graham R.,
_d-2007.
_e1
245 1 0 _aIntroduction to Banach spaces and algebras /Graham Allan ; prepared for publication by H. Garth Dales.
260 _aOxford :
_bOxford University Press,
_c(c)2011.
300 _a1 online resource (vii, 371 pages)
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _adata file
_2rda
490 1 _aOxford graduate texts in mathematics ;
_v20
504 _a2
520 3 _aBanach spaces and algebras are a key topic of pure mathematics. Graham Allan's careful and detailed introductory account will prove essential reading for anyone wishing to specialise in functional analysis and is aimed at final year undergraduates or masters level students. Based on the author's lectures to fourth year students at Cambridge University, the book assumes knowledge typical of first degrees in mathematics, including metric spaces, analytic topology, and complex analysis. However, readers are not expected to be familiar with the Lebesgue theory of measure and integration. The text begins by giving the basic theory of Banach spaces, including dual spaces and bounded linear operators. It establishes forms of the theorems that are the pillars of functional analysis, including the Banach-Alaoglu, Hahn-Banach, uniform boundedness, open mapping, and closed graph theorems. There are applications to Fourier series and operators on Hilbert spaces. The main body of the text is an introduction to the theory of Banach algebras. A particular feature is the detailed account of the holomorphic functional calculus in one and several variables; all necessary background theory in one and several complex variables is fully explained, with many examples and applications considered. Throughout, exercises at sections ends help readers test their understanding, while extensive notes point to more advanced topics and sources.
505 0 0 _apart I. Introduction to Banach spaces. 1. Preliminaries --
_t2. Elements of normed spaces --
_t3. Banach spaces --
_tpart II. Introduction to Banach algebras. 4. Banach algebras --
_t5. Representation theory --
_t6. Algebras with an involution --
_t7. The Borel functional calculus --
_tpart III. Several complex variables and Banach algebras. 8. Introduction to several complex variables --
_t9. The holomorphic functional calculus in several variables.
530 _a2
_ub
650 0 _aBanach spaces.
650 0 _aBanach algebras.
655 1 _aElectronic Books.
700 1 _aDales, H. G.
_d1944-
700 1 _q(Harold G.),
856 4 0 _uhttps://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=655428&site=eds-live&custid=s3260518
_zClick to access digital title | log in using your CIU ID number and my.ciu.edu password
942 _cOB
_D
_eEB
_hQA.
_m2011
_QOL
_R
_x
_8NFIC
_2LOC
994 _a02
_bNT
999 _c100324
_d100324
902 _a1
_bCynthia Snell
_c1
_dCynthia Snell