Natural conditions on the spectra of operators
Document Type
Article
Publication Date
6-1993
Abstract
Natural conditions are imposed on spectra of products and sums of operators. This results in characterizations of positive operators, Hermitian operators, compact operators, and unitary operators. Here are two main results: If S is an operator and the spectrum of ST consists of nonnegative real numbers for all invertible positive operators [noninvertible positive operators] T, then S is a positive operator. If S is an operator and the spectrum of ST is countable for all invertible operators [noninvertible operators] T, then S is a compact operator. The first half of the paper is primarily concerned with operators on finite-dimensional spaces, and the second half with operators on infinite-dimensional Hilbert spaces.
Publication Title
Linear Algebra and its Applications
Volume
186
First Page
183
Last Page
197
Digital Object Identifier (DOI)
https://doi.org/10.1016/0024-3795(93)90290-5
Citation Information
Hochwald, S. H. (1993). Natural conditions on the spectra of operators. Linear Algebra and Its Applications, 186, 183–197. https://doi.org/10.1016/0024-3795(93)90290-5