Spatial Numerical Ranges of Elements of Banach Algebras
DOI
10.1155/S0161171289000785
Document Type
Journal Article
Publication Date
1-1-1989
Publication Title
International Journal of Mathematics and Mathematical Sciences
Volume
12
Issue
4
First Page
633
Last Page
640
ISSN
1611712
Keywords
numerical ranges, regular norm of a normed or Banach algebra, Spatial numerical ranges, spectrum
Abstract
In this paper, the notion of spatial numerical range of elements of Banach algebras without identity is studied. Specifically, the relationship between spatial numerical ranges, numerical ranges and spectra is investigated. Among other results, it is shown that the closure of the spatial numerical range of an element of a Banach algebra without identity but with regular norm is exactly its numerical range as an element of the unitized algebra. Futhermore, the closure of the spatial numerical range of a hermitian element coincides with the convex hull of its spectrum. In particular, spatial numerical ranges of the elements of the Banach algebra Co(X) are described. © 1989, Hindawi Publishing Corporation. All right reserved.
Open Access
Gold
Repository Citation
Gaur, A., & Husain, T. (1989). Spatial Numerical Ranges of Elements of Banach Algebras. International Journal of Mathematics and Mathematical Sciences, 12 (4), 633-640. https://doi.org/10.1155/S0161171289000785