Taylor and Francis Ltd.;Abingdon: Taylor & Francis Group
摘要:
摘要： We show that (1) if A is a nonzero quasinilpotent operator with ran A n closed for some n ≥ 1, then its numerical range W(A) contains 0 in its interior and has a differentiable boundary, and (2) a noncircular elliptic disc can be the numerical range of a nilpotent operator with nilpotency 3 on an infinite-dimensional separable space. (1) is a generalization of the known result for nonzero nilpotent operators, and (2) is in contrast to the finite-dimensional case, where the only elliptic discs which are the numerical ranges of nilpotent finite matrices are the circular ones centred at the origin. 出版者： Abingdon: Taylor & Francis Group 出版日期： 2012-11 出處： Linear & multilinear algebra, 2012-11, Vol.60 (11-12), p.1225-1233 版權： Copyright Taylor & Francis Group, LLC 2012 版權： Copyright Taylor and Francis Group, LLC 識別號： ISSN: 0308-1087 識別號： EISSN: 1563-5139 識別號： DOI: 10.1080/03081087.2011.611945
