×

Skew symmetric weighted shifts. (English) Zbl 1310.47045

Summary: An operator \(T\) on a complex Hilbert space \(\mathcal{H}\) is called skew symmetric if \(T\) can be represented as a skew symmetric matrix relative to some orthonormal basis for \(\mathcal{H}\). We first give a canonical decomposition for general skew symmetric operators. Based on this decomposition, we provide a classification of skew symmetric weighted shifts.

MSC:

47B37 Linear operators on special spaces (weighted shifts, operators on sequence spaces, etc.)
47B99 Special classes of linear operators
47A05 General (adjoints, conjugates, products, inverses, domains, ranges, etc.)
PDF BibTeX XML Cite
Full Text: DOI Euclid