Abstract
In a finite-dimensional unitary space, the notion of a sesquilinear form and that of a linear operator are equivalent, symmetric forms corresponding to symmetric operators. This is true even in an infinite-dimensional Hilbert space as long as one is concerned with bounded forms and bounded operators. When we have to consider unbounded forms and operators, however, there is no such obvious relationship. Nevertheless there exists a closed theory on a relationship between semibounded symmetric forms and semibounded selfadjoint operators1. This theory can be extended to non-symmetric forms and operators within certain restrictions. Since the results are essential in applications to perturbation theory, a detailed exposition of them will be given in this chapter2. Some of the immediate applications are included here, and further results will be found in Chapters VII and VIII.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1995 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Kato, T. (1995). Sesquilinear forms in Hilbert spaces and associated operators. In: Perturbation Theory for Linear Operators. Classics in Mathematics, vol 132. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-66282-9_6
Download citation
DOI: https://doi.org/10.1007/978-3-642-66282-9_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-58661-6
Online ISBN: 978-3-642-66282-9
eBook Packages: Springer Book Archive