000 | 03349nam a2200397Ki 4500 | ||
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001 | ocn861693022 | ||
003 | OCoLC | ||
005 | 20240726105433.0 | ||
008 | 131029s2011 enk ob 001 0 eng d | ||
040 |
_aNT _beng _erda _epn _cNT |
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020 |
_a9780191548543 _q((electronic)l(electronic)ctronic)l((electronic)l(electronic)ctronic)ctronic bk. |
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050 | 0 | 4 |
_aQA322 _b.I587 2011 |
049 | _aNTA | ||
100 | 1 |
_aAllan, Graham R., _d-2007. _e1 |
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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. |
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300 | _a1 online resource (vii, 371 pages) | ||
336 |
_atext _btxt _2rdacontent |
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337 |
_acomputer _bc _2rdamedia |
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_aonline resource _bcr _2rdacarrier |
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_adata file _2rda |
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490 | 1 |
_aOxford graduate texts in mathematics ; _v20 |
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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. |
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_a2 _ub |
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650 | 0 | _aBanach spaces. | |
650 | 0 | _aBanach algebras. | |
655 | 1 | _aElectronic Books. | |
700 | 1 |
_aDales, H. G. _d1944- |
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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 |
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_a02 _bNT |
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_c100324 _d100324 |
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902 |
_a1 _bCynthia Snell _c1 _dCynthia Snell |