000			02176nam a2200241Ia 4500
003			OSt
005			20250916114359.0
008			220909b |||||||| |||| 00| 0 eng d
020			_a9780821820650
040			_aCSL _beng _cCSL
041			_aeng.
084			_aB48 P0 TB _qCSL
100			_aConway, J R _eauthor. _9821504
245		0	_aCourse in Operator Theory
260			_aRhode : _bIsland AMS, _c2000.
300			_axv, 372p.
500			_aIncludes Bibliography 335-366p.; Index 367-370p.
520			_a Operator theory is a significant part of many important areas of modern mathematics: functional analysis, differential equations, index theory, representation theory, mathematical physics, and more. This text covers the central themes of operator theory, presented with the excellent clarity and style that readers have come to associate with Conway's writing. Early chapters introduce and review material on C*-algebras, normal operators, compact operators and non-normal operators. The topics include the spectral theorem, the functional calculus and the Fredholm index. Also, some deep connections between operator theory and analytic functions are presented.Later chapters cover more advanced topics, such as representations of C*-algebras, compact perturbations and von Neumann algebras. Major results, such as the Sz.-Nagy Dilation Theorem, the Weyl-von Neumann-Berg Theorem and the classification of von Neumann algebras, are covered, as is a treatment of Fredholm theory. These advanced topics are at the heart of current research. The last chapter gives an introduction to reflexive subspaces, i.e., subspaces of operators that are determined by their invariant subspaces. These, along with hyperreflexive spaces, are one of the more successful episodes in the modern study of asymmetric algebras. Professor Conway's authoritative treatment makes this a compelling and rigorous course text, suitable for graduate students who have had a standard course in functional analysis.
650			_aMathematics. _9821505
650			_aOperator theory. _9821506
942			_hB48 P0 TB _cTB _2CC _n0
999			_c15724 _d15724