000			02348nam a22002657a 4500
003			OSt
005			20241025114540.0
008			190404b ||||| |||| 00| 0 eng d
020			_a9781461381556
040			_cTata Book House _aICTS-TIFR
050			_aQA320
100			_aA. A. Kirillov
245			_aTheorems and problems in functional analysis
260			_aNew York: _bSpringer-Verlag, _c[c1982]
300			_a347 p.
490			_a Problem Books in Mathematics
505			_aChapter 1. Concepts from Set Theory and Topology Chapter 2. Theory of Measures and Integrals Chapter 3. Linear Topological Spaces and Linear Operators Chapter 4. The Fourier Transformation and Elements of Harmonic Analysis Chapter 5. The Spectral Theory of Operators
520			_aThe algebraic approach to the study of the real line involves describing its properties as a set to whose elements we can apply" operations," and obtaining an algebraic model of it on the basis of these properties, without regard for the topological properties. On the other hand, we can focus on the topology of the real line and construct a formal model of it by singling out its" continuity" as a basis for the model. Analysis regards the line, and the functions on it, in the unity of the whole system of their algebraic and topological properties, with the fundamental deductions about them obtained by using the interplay between the algebraic and topological structures. The same picture is observed at higher stages of abstraction. Algebra studies linear spaces, groups, rings, modules, and so on. Topology studies structures of a different kind on arbitrary sets, structures that give mathe­ matical meaning to the concepts of a limit, continuity, a neighborhood, and so on. Functional analysis takes up topological linear spaces, topological groups, normed rings, modules of representations of topological groups in topological linear spaces, and so on. Thus, the basic object of study in functional analysis consists of objects equipped with compatible algebraic and topological structures.---Summary provided by publisher
650			_aMathematics
700			_aA. D. Gvishiani
700			_aTranslated by Harold H.McFaden
700			_aEdited by P.R Halmous
856			_uhttps://link.springer.com/book/10.1007/978-1-4613-8153-2#toc
942			_2lcc _cBK
999			_c2587 _d2587