Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Completely seminormal operators with boundary eigenvalues

Author: Kevin Clancey
Journal: Trans. Amer. Math. Soc. 182 (1973), 133-143
MSC: Primary 47B37
MathSciNet review: 0341167
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: For $ f \in {L^2}(E)$ we consider the singular integral operator $ {T_E}f(s) = sf(s) + {\pi ^{ - 1}}{\smallint _E}f(t){(t - s)^{ - 1}}dt$. These singular integral operators are a special case of operators acting on a Hilbert space with one dimensional self-commutator. We discover generalized eigenfunctions of the equation $ {T_E}f = 0$ and, for $ p < 2$, we will give an $ {L^p}(E)$ solution of the equation $ {T_E}f = {\chi _E}$. The main result of the paper is an example of a nonzero $ {L^2}(E)$ solution of $ {T_E}f = 0$, with $ \lambda = 0$ a boundary point of the spectrum of $ {T_E}$.

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

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 47B37

Retrieve articles in all journals with MSC: 47B37

Additional Information

Keywords: Singular integral operator, seminormal operator
Article copyright: © Copyright 1973 American Mathematical Society

American Mathematical Society