# Hokkaido Mathematical Journal

## Hokkaido Mathematical Journal, 35 (2006) pp.247-259

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### Abstract

Let $T$ be a semi-hyponormal operator on a complex separable Hilbert space. In this paper, we give Helton-Howe type trace formulae of smooth functions associated with the polar decomposition $T = U|T|$ and improve Theorem 10 of [5] by this result.

MSC(Primary) 47B20 47A10 Hilbert space, operator, trace, principal function