Banach Algebra Techniques in Operator TheorySpringer Science & Business Media, 27 ביולי 1998 - 198 עמודים Operator theory is a diverse area of mathematics which derives its impetus and motivation from several sources. It began with the study of integral equations and now includes the study of operators and collections of operators arising in various branches of physics and mechanics. The intention of this book is to discuss certain advanced topics in operator theory and to provide the necessary background for them assuming only the standard senior-first year graduate courses in general topology, measure theory, and algebra. At the end of each chapter there are source notes which suggest additional reading along with giving some comments on who proved what and when. In addition, following each chapter is a large number of problems of varying difficulty. This new edition will appeal to a new generation of students seeking an introduction to operator theory. |
תוכן
Banach Algebras | 30 |
Abstract Index in a Banach Algebra | 33 |
The Space of Multiplicative Linear Functions | 36 |
The Gelfand Transform | 37 |
The GelfandMazur Theorem | 39 |
The Gelfand Theorem for Commutative Banach Algebras | 41 |
The Spectral Radius Formula | 42 |
The StoneWeierstrass Theorem | 43 |
WAlgebras | 92 |
Isomorphisms of LSpaces | 94 |
Normal Operators with Cyclic Vectors | 95 |
Maximal Abelian WAlgebras | 98 |
Homomorphisms of CAlgebras | 100 |
The Extended Functional Calculus | 102 |
The Fuglede Theorem | 103 |
Notes | 104 |
The Generalized StoneWeierstrass Theorem | 46 |
The Disk Algebra | 47 |
The Algebra of Functions with Absolutely Convergent Fourier Series | 50 |
The Algebra of Bounded Measurable Functions | 52 |
Notes | 53 |
Geometry of Hilbert Space | 58 |
The CauchySchwarz Inequality | 59 |
The Pythagorean Theorem | 60 |
Hilbert Spaces | 61 |
The Riesz Representation Theorem | 66 |
The Existence of Orthonormal Bases | 69 |
The Dimension of Hilbert Spaces | 70 |
Notes | 71 |
Operators on Hilbert Space and CAlgebras | 74 |
Normal and Selfadjoint Operators | 77 |
Projections and Subspaces | 78 |
Multiplication Operators and Maximal Abelian Algebras | 80 |
The Bilateral Shift Operator | 82 |
CAlgebras | 83 |
The GelfandNaimark Theorem | 84 |
The Spectral Theorem | 85 |
The Square Root of Positive Operators | 86 |
The Unilateral Shift Operator | 87 |
The Polar Decomposition | 88 |
Weak and Strong Operator Topologies | 91 |
Compact Operators Fredholm Operators and Index Theory | 108 |
Approximation of Compact Operators | 110 |
Integral Operators | 112 |
The Calkin Algebra and Fredholm Operators | 113 |
Atkinsons Theorem | 114 |
The Index of Fredholm Operators | 115 |
The Fredholm Alternative | 116 |
Volterra Integral Operators | 118 |
Connectedness of the Unitary Group in a WAlgebra | 119 |
Quotient CAlgebras | 124 |
Representations of the CAlgebra of Compact Operators | 126 |
Notes | 129 |
The Hardy Spaces | 133 |
Reducing Subspaces of Unitary Operators | 135 |
Beurlings Theorem | 137 |
The Maximal Ideal Space of H | 138 |
The InnerOuter Factorization of Functions in H2 | 141 |
The Conjugates of H¹ and LHo | 144 |
The Closedness of H+C | 145 |
The GleasonWhitney Theorem | 149 |
Toeplitz Operators | 158 |
185 | |
191 | |
מהדורות אחרות - הצג הכל
Banach Algebra Techniques in Operator Theory <span dir=ltr>Ronald G. Douglas</span> תצוגה מקדימה מוגבלת - 2012 |
מונחים וביטויים נפוצים
Banach space bounded variation C*-algebra Cauchy sequence closed subspace closure commutative Banach algebra compact Hausdorff space compact operator completes the proof contained continuous function converges Corollary defined Definition denote dense element exists extension finite dimensional follows Fredholm operator function ƒ function in L∞(T functional calculus ƒ and g ƒ in H Gelfand transform Hausdorff space hence Hilbert space Hint homomorphism implies inner function inner product isometric isomorphism l¹(Z LC(H Lemma linear space linear transformation mapping Math maximal ideal maximal ideal space Moreover multiplicative linear functional nonzero norm normal operator obtain operator on H orthogonal orthonormal basis outer function partial isometry polynomials preceding proof is complete Proposition result Riesz self-adjoint subalgebra space H spectrum subalgebra of C(X subset Theorem Toeplitz operators unit ball unitary operator v₁ w*-topology weak operator topology ΕΑ
קטעים בולטים
עמוד 186 - LA Coburn and RG Douglas, Translation operators on the half-line, Proc. Nat. Acad. Sci. USA 62, 1010-1013 (1969).
עמוד 186 - RG Douglas and W. Rudin, Approximation by inner functions, Pacific J. Math. 31 (1969), 313-320.
עמוד 186 - RG DOUGLAS AND C. PEARCY, Spectral theory of generalized Toeplitz operators, Trans. Amer. Math. Soc. 115 (1965), 433-444.
הפניות לספר זה
Loop Groups <span dir=ltr>Andrew Pressley</span>,<span dir=ltr>Graeme Segal</span> אין תצוגה מקדימה זמינה - 1988 |
Completely Bounded Maps and Operator Algebras <span dir=ltr>Vern Paulsen</span> תצוגה מקדימה מוגבלת - 2002 |