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41. Introduction to Spectral Theory: With Applications to Schrödinger Operators (Applied Mathematical Sciences) by P.D. Hislop, I.M. Sigal | |
Hardcover: 352
Pages
(1995-11-16)
list price: US$115.00 -- used & new: US$84.75 (price subject to change: see help) Asin: 0387945016 Canada | United Kingdom | Germany | France | Japan | |
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42. Operator Theory, Systems Theory and Scattering Theory: Multidimensional Generalizations (Operator Theory: Advances and Applications) | |
Hardcover: 310
Pages
(2005-05-31)
list price: US$169.00 -- used & new: US$18.70 (price subject to change: see help) Asin: 3764372125 Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Operator theory, system theory, scattering theory, and the theory of analytic functions of one complex variable are deeply related topics, and the relationships between these theories are well understood. When one leaves the setting of one operator and considers several operators, the situation is much more involved. There is no longer a single underlying theory, but rather different theories, some of them loosely connected and some not connected at all. These various theories, which one could call "multidimensional operator theory", are topics of active and intensive research. |
43. A Short Course on Spectral Theory (Graduate Texts in Mathematics) by William Arveson | |
Paperback: 135
Pages
(2010-11-02)
list price: US$59.95 -- used & new: US$18.99 (price subject to change: see help) Asin: 1441929436 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (2)
Great author! The book is 130p only, so it might be ideal for self study. Not everything is in the text but if you want to try the exercises (you might need further reading to do some of them) and you do the extra reading from other sources, you will end up getting a good understanding. The chapters are: 1. Spectral theory and Banach algebras, 2. Operators on Hilbert space, 3. Asymptotics: Compact perturbations and Fredholm theory and 4. Methods and applications approximatelly 170 exercises. The most inspiring book on the subject I have seen, up to now.
A book to learn from. |
44. C*-Algebras and Operator Theory by Gerard J. Murphy | |
Hardcover: 296
Pages
(1990-09-11)
list price: US$114.00 -- used & new: US$91.19 (price subject to change: see help) Asin: 0125113609 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (1)
Excellent, modern introduction to C*-algebras Spectral theory is introduced in chapter 1, with a definition of Banach algebras immediately given on the first page. There are many advantages is presenting spectral theory in this general context, and the author illustrates these advantages throughout the chapter. For Banach algebras with a unit, Gelfand's theorem, giving the non-emptiness of the spectrum, is proven. The author also discusses the Gelfand representation, that says essentially that abelian Banach algebras act like continuous functions. He then restricts his attention to compact and Fredholm operators, and discusses their index theory. It is here that the reader can see the origin of the idea of a compact operator acting as a "zero element" in algebras of operators. This is readily apparent in the definition of the Calkin algebra, which is the quotient algebra modulo the compact operators. The theory of von Neumann algebras, or W*-algebras as they are sometimes called, is discussed in chapter 4. His viewpoint of them is characteristically modern, as essentially a noncommutative measure theory. This viewpoint meshes will with current research in the field of noncommutative geometry. Proofs of the double commutant theorem and the Kaplansky density theorem are given. The presence of the weak operator topology makes these objects of primary interest to applications in quantum physics, as it is this topology which is physically relevant. The famous "type" characterization of projections in von Neumann algebras is given in an addendum to the chapter. The representation theory of C*-algebras is considered in chapter 5. The author shows that topological irreducibility is equivalent to algebraic irreducibility for C*-algebras. The reader can see the role that ideals, especially the "primitive" ideals, play in the representation theory. The author also discusses CCR algebras, but he calls them "liminal" algebras. The theory of liminal algebras is of upmost importance in applications to quantum physics (physicists still call them CCR algebras). Chapter 6 is an introduction to the construction of C*-algebras using direct limits and tensor products of given C*-algebras. And here again, the physicist reader will find a useful class of algebras, namely the AF-algebras, which are used heavily in mathematical statistical mechanics. Nuclear C*-algebras, which are the most well-behaved class under the operation of tensor product, are discussed briefly. The last chapter of the book is the most interesting, for it deals with the K-theory of C*-algebras. The Brown-Douglas-Fillmore theory was briefly mentioned in an addendum to chapter 2. This theory could be considered a precursor to latter work on K-theory of operator algebras. The author explains the origin of the K-groups K0(A) and K1(A) assigned to a C*-algebra, and how they can be used to study some properties of A. The K-groups are constructed by first forming the set P(A) consisting of the union of all projections in the collection of n by n matrices over an arbitrary *-algebra A. Then for a unital *-algebra A, a notion of stable equivalance is defined for elements of P(A). The reader familiar with the K-theory of vector bundles will see the similarity in this definition. Here the two projections are stably equivalent if they are equivalent under the direct sum of the n x n identity operator. The equivalance classes under stability are then enveloped via the Grothendieck group, giving the K-group K0(A). Then the K0-group shown to be a complete isomorphism invariant for unital AF-algebras, i.e. two unital AF-algebras are *-isomorphic iff there is a unital order isomorphism between their K0-groups. Three fundamental results in K-theory are then discussed: "weak exactness", which gives an exact sequence of K0-groups given an exact sequence of C*-algebras; "homotopy invariance", which shows that mappings between the K0-groups of two C*-algebras are equal if the mappings between the C*-algebras are homotopic; "continuity": which gives a notion of continuity for the K0-functor. Then after defining a notion of stability for the K0-functor, the author proves an analog of Bott periodicity. This involves of course the construction of the K1-group, which is done in terms of the suspension of the C*-algebra, in complete analogy with the vector bundle case. ... Read more |
45. Topics in the Theory of Schrodinger Operators | |
Hardcover: 288
Pages
(2004-05-31)
list price: US$107.00 -- used & new: US$70.00 (price subject to change: see help) Asin: 9812387978 Canada | United Kingdom | Germany | France | Japan | |
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46. The Ordered Weighted Averaging Operators: Theory and Applications | |
Hardcover: 357
Pages
(1997-05-31)
list price: US$259.00 -- used & new: US$205.57 (price subject to change: see help) Asin: 079239934X Canada | United Kingdom | Germany | France | Japan | |
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47. Treatise on the Shift Operator: Spectral Function Theory (Grundlehren der mathematischen Wissenschaften) by N.K. Nikol'skii | |
Hardcover: 491
Pages
(1986-02-14)
list price: US$183.00 -- used & new: US$183.00 (price subject to change: see help) Asin: 3540150218 Canada | United Kingdom | Germany | France | Japan | |
48. Operators and Representation Theory: Canonical Models for Algebras of Operators Arising in Quantum Mechanics (Dover Books on Physics) by Palle E.T. Jorgensen | |
Paperback: 352
Pages
(2008-05-19)
list price: US$19.95 -- used & new: US$11.75 (price subject to change: see help) Asin: 0486466655 Canada | United Kingdom | Germany | France | Japan | |
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49. An Introduction to Models and Decompositions in Operator Theory by Carlos S. Kubrusly | |
Hardcover: 148
Pages
(1997-08-19)
list price: US$84.95 -- used & new: US$14.99 (price subject to change: see help) Asin: 0817639926 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (1)
Nice and well organized introduction to a difficult subject |
50. Theory of Operator Algebras II by Masamichi Takesaki | |
Hardcover: 450
Pages
(2002-12-16)
list price: US$149.00 -- used & new: US$118.31 (price subject to change: see help) Asin: 354042914X Canada | United Kingdom | Germany | France | Japan | |
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51. Basic Classes of Linear Operators by Israel Gohberg, Seymour Goldberg, Marinus A. Kaashoek | |
Paperback: 423
Pages
(2004-01-12)
list price: US$129.00 -- used & new: US$87.89 (price subject to change: see help) Asin: 3764369302 Canada | United Kingdom | Germany | France | Japan | |
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52. Jordan Algebras in Analysis, Operator Theory, and Quantum Mechanics (Cbms Regional Conference Series in Mathematics) by Harald Upmeier | |
Paperback: 85
Pages
(1987-12-31)
list price: US$21.00 -- used & new: US$20.99 (price subject to change: see help) Asin: 082180717X Canada | United Kingdom | Germany | France | Japan | |
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53. Geometry of State Spaces of Operator Algebras (Mathematics: Theory & Applications) by Erik M. Alfsen, Frederic W. Shultz | |
Hardcover: 488
Pages
(2002-12-13)
list price: US$99.00 -- used & new: US$65.99 (price subject to change: see help) Asin: 0817643192 Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Key features include: * The properties used to describe state spaces are primarily of a geometric nature, but many can also be interpreted in terms of physics. There are numerous remarks discussing these connections * A quick introduction to Jordan algebras is given; no previous knowledge is assumed and all necessary background on the subject is given * A discussion of dynamical correspondences, which tie together Lie and Jordan structures, and relate the observables and the generators of time evolution in physics * The connection with Connes' notions of orientation and homogeneity in cones is explained * Chapters conclude with notes placing the material in historical context * Prerequisites are standard graduate courses in real and complex variables, measure theory, and functional analysis * Excellent bibliography and index In the authors' previous book, "State Spaces of Operator Algebras: Basic Theory, Orientations and C*-products" (ISBN 0-8176-3890-3), the role of orientations was examined and all the prerequisites on C*-algebras and von Neumann algebras, needed for this work, were provided in detail. These requisites, as well as all relevant definitions and results with reference back to "State Spaces," are summarized in an appendix, further emphasizing the self-contained nature of this work. "Geometry of State Spaces of Operator Algebras" is intended for specialists in operator algebras, as well as graduate students and mathematicians in other areas. |
54. Modern Mathematical Methods in Transport Theory (Operator Theory Advances and Applications) by W. Greenberg | |
Hardcover: 340
Pages
(1991-02-22)
list price: US$152.00 -- used & new: US$433.86 (price subject to change: see help) Asin: 0817625712 Canada | United Kingdom | Germany | France | Japan | |
55. Hilbert Space Operators in Quantum Physics (Theoretical and Mathematical Physics) by Jirí Blank, Pavel Exner, Miloslav Havlícek | |
Paperback: 664
Pages
(2010-11-30)
list price: US$139.00 -- used & new: US$110.66 (price subject to change: see help) Asin: 9048180120 Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description This course-tested book explains in detail the theory of linear Hilbert-space operators and their use in quantum physics. The central mathematical tool of the book is the spectral theory of self-adjoint operators; in order to make the exposition self-contained, selected topics of functional analysis are included. An introduction to the theory of operator sets and algebras is also presented. This mathematical material is then used for a systematic analysis of the operator structure of quantum theory. Logical building of the theory is discussed as well as its practical aspects, such as spectral properties of quantum mechanical Hamiltonians, scattering theory, and more. The second edition was extended by two new chapters devoted to properties of quantum waveguides and quantum graphs. The bibliography was amended by about 130 new items. |
56. Operator Theory and Systems: PROCEEDINGS WORKSHOP Amsterdam 4.-7.6.1985 (Operator Theory: Advances and Applications) by Bart, Gohberg, Kaashoek | |
Hardcover: 475
Pages
(2000-06-06)
list price: US$189.00 -- used & new: US$189.00 (price subject to change: see help) Asin: 3764317833 Canada | United Kingdom | Germany | France | Japan | |
57. Operator Theory, System Theory and Related Topics: The Moshe Livsic Anniversary Volume (Operator Theory: Advances and Applications) | |
Hardcover: 567
Pages
(2001-04-20)
list price: US$259.00 -- used & new: US$259.00 (price subject to change: see help) Asin: 3764365234 Canada | United Kingdom | Germany | France | Japan | |
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58. Spectral Theory of Linear Differential Operators and Comparison Algebras (London Mathematical Society Lecture Note Series) by Heinz Otto Cordes | |
Paperback: 356
Pages
(1987-04-24)
list price: US$99.99 -- used & new: US$84.98 (price subject to change: see help) Asin: 0521284430 Canada | United Kingdom | Germany | France | Japan | |
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59. Operator Theory and Arithmetic in $H^\infty$ (Mathematical Surveys and Monographs) by Hari Bercovici | |
Hardcover: 275
Pages
(1988-12-31)
list price: US$95.00 -- used & new: US$87.48 (price subject to change: see help) Asin: 0821815288 Canada | United Kingdom | Germany | France | Japan | |
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60. Topics in Operator Theory: Ernst d Hellinger Memorial Volume (Operator Theory Advances and Applications) by L. De Branges, I. Gohberg | |
Hardcover: 464
Pages
(1990-11-02)
list price: US$185.00 -- used & new: US$520.49 (price subject to change: see help) Asin: 0817625321 Canada | United Kingdom | Germany | France | Japan | |
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