| eBook ISBN: | 978-1-4704-0099-6 |
| Product Code: | MEMO/109/522.E |
| List Price: | $40.00 |
| MAA Member Price: | $36.00 |
| AMS Member Price: | $24.00 |
| eBook ISBN: | 978-1-4704-0099-6 |
| Product Code: | MEMO/109/522.E |
| List Price: | $40.00 |
| MAA Member Price: | $36.00 |
| AMS Member Price: | $24.00 |
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Book DetailsMemoirs of the American Mathematical SocietyVolume: 109; 1994; 103 ppMSC: Primary 47; 46
Principal currents were invented to provide a noncommutative spectral theory in which there is still significant localization. These currents are often integral and are associated with a vector field and an integer-valued weight which plays the role of a multi-operator index. The study of principal currents involves scattering theory, new geometry associated with operator algebras, defect spaces associated with Wiener-Hopf and other integral operators, and the dilation theory of contraction operators. This monograph explores the metric geometry of such currents for a pair of unitary operators and certain associated contraction operators. Applications to Toeplitz, singular integral, and differential operators are included.
ReadershipOperator theorists, functional analysts and possibly graduate students.
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Table of Contents
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Chapters
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0. Introduction
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1. The geometry associated with eigenvalues
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2. The dilation space solution of the symbol Riemann Hilbert problem
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3. The principal current for the operator-tuple $\{P_1, P_2, W_1, W_2\}$
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4. Estimates
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5. The criterion for eigenvalues
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6. The $N(\omega )$ operator
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7. The characteristic operator function of $T_1$
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8. Localization and the “cut-down” property
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9. The joint essential spectrum
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10. Singular integral representations
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11. Toeplitz operators with unimodular symbols
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12. $C_{11}$-contraction operators with (1,1) deficiency indices
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Principal currents were invented to provide a noncommutative spectral theory in which there is still significant localization. These currents are often integral and are associated with a vector field and an integer-valued weight which plays the role of a multi-operator index. The study of principal currents involves scattering theory, new geometry associated with operator algebras, defect spaces associated with Wiener-Hopf and other integral operators, and the dilation theory of contraction operators. This monograph explores the metric geometry of such currents for a pair of unitary operators and certain associated contraction operators. Applications to Toeplitz, singular integral, and differential operators are included.
Operator theorists, functional analysts and possibly graduate students.
-
Chapters
-
0. Introduction
-
1. The geometry associated with eigenvalues
-
2. The dilation space solution of the symbol Riemann Hilbert problem
-
3. The principal current for the operator-tuple $\{P_1, P_2, W_1, W_2\}$
-
4. Estimates
-
5. The criterion for eigenvalues
-
6. The $N(\omega )$ operator
-
7. The characteristic operator function of $T_1$
-
8. Localization and the “cut-down” property
-
9. The joint essential spectrum
-
10. Singular integral representations
-
11. Toeplitz operators with unimodular symbols
-
12. $C_{11}$-contraction operators with (1,1) deficiency indices
