## 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.)
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