Principal currents for a pair of unitary operators / Joel D. Pincus, Shaojie Zhou.

Format:

Book

Author/Creator:

Pincus, Joel D., 1934- author.

Zhou, Shaojie, 1960- author.

Series:

Memoirs of the American Mathematical Society ; Volume 57, Number 329.

Memoirs of the American Mathematical Society, 0065-9266 ; Volume 109, Number 522

Language:

English

Subjects (All):

Subnormal operators.

Geometric measure theory.

C*-algebras.

Decomposition (Mathematics).

Physical Description:

1 online resource (114 p.)

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, 1994.

Language Note:

English

Summary:

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.

Contents:

""Contents""; ""Â0. Introduction""; ""Â1. The geometry associated with eigenvalues""; ""Â2. The dilation space solution of the symbol Riemann Hilbert problem""; ""Â3. The principal current for the operator-tuple {P[sub(1)], P[sub(2)], W[sub(1)],W[sub(2)]}""; ""Â4. Estimates""; ""Â5. The criterion for eigenvalues""; ""Â6. The N(w) operator""; ""Â7. The characteristic operator function of T[sub(1)]""; ""Â8. Localization and the ""cut-down"" property""; ""Â9. The joint essential spectrum""; ""Â10. Singular integral representations""

""Â11. Toeplitz operators with unimodular symbols""""Â12. C[sub(11)]-Contraction operators with (1,1) deficiency indices""; ""Â13. Appendix A""; ""Â14. Appendix B""; ""Â15. Appendix C""; ""References""

Notes:

"May 1994, Volume 109, Number 522 (second of 5 numbers)."

Includes bibliographical references.

Description based on print version record.

ISBN:

1-4704-0099-5