Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)


Hyponormal operators having real parts with simple spectra

Author: C. R. Putnam
Journal: Trans. Amer. Math. Soc. 172 (1972), 447-464
MSC: Primary 47B20
MathSciNet review: 0310689
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ {T^ \ast }T - T{T^ \ast } = D \geq 0$ and suppose that the real part of $ T$ has a simple spectrum. Then $ D$ is of trace class and $ \pi $ trace$ (D)$ is a lower bound for the measure of the spectrum of $ T$. This latter set is specified in terms of the real and imaginary parts of $ T$. In addition, the spectra are determined of self-adjoint singular integral operators on $ {L^2}(E)$ of the form $ A(x)f(x) + \Sigma {b_j}(x)H[f{\bar b_j}](x)$, where $ E \ne ( - \infty ,\infty ),A(x)$ is real and bounded, $ \Sigma \vert{b_j}(x){\vert^2}$ is positive and bounded, and $ H$ denotes the Hilbert transform.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 47B20

Retrieve articles in all journals with MSC: 47B20

Additional Information

PII: S 0002-9947(1972)0310689-0
Keywords: Hyponormal operators, measure of the spectrum of a hyponormal operator, simple spectra, absolute continuity of operators, trace class operators, spectra of singular integral operators
Article copyright: © Copyright 1972 American Mathematical Society