Title: | Higher-dimensional numerical ranges of quadratic operators |
Authors: | Chien, MT Tso, SH Wu, PY 應用數學系 Department of Applied Mathematics |
Keywords: | k-numerical range;square-zero operator;idempotent operator;quadric operator |
Issue Date: | 1-Dec-2003 |
Abstract: | We show that for every positive integer k, the k-numerical range of a square-zero operator on a (separable) Hilbert space is an (open or closed) circular disc centered at the origin. The radius and the closedness of the disc can be completely determined in terms of the "singular numbers" of the operator. The k-numerical range of idempotent operators is more difficult to describe since its boundary is in general not any familiar curve. What we do is to give enough information, again in terms of the singular numbers of the idempotent operator under consideration, so as to have a general idea of its shape and location. |
URI: | http://hdl.handle.net/11536/27342 |
ISSN: | 0379-4024 |
Journal: | JOURNAL OF OPERATOR THEORY |
Volume: | 49 |
Issue: | 1 |
Begin Page: | 153 |
End Page: | 171 |
Appears in Collections: | Articles |