Publications in Scientific Journals:

W. Auzinger:
"Sectorial operators and normalized numerical range";
Applied Numerical Mathematics, 45 (2003), 367 - 388.

English abstract:
We study the notion of sectorial operator in a Hilbert space. According to the classical definition, the numerical range R(A) of a sectorial operator A is contained in a sector Sσ = { z in C: |Arg z| <= σ }, and this is equivalent to a certain inverse estimate valid outside Sσ. In this paper we show that the validity of the same estimate, but with a factor >1 , is equivalent to the validity of a certain strengthened Cauchy-Schwarz inequality for all pairs w,Aw. This extends the original characterization in terms of R(A) by a more general characterization based on a normalized numerical range RN(A). We also show how RN(A) can be computed numerically.

"Official" electronic version of the publication (accessed through its Digital Object Identifier - DOI)

Online library catalogue of the TU Vienna:

Electronic version of the publication:

Created from the Publication Database of the Vienna University of Technology.