Commuting hyponormal operators

James Guyker

Vol. 91 (1980), No. 2, 307–325

DOI: 10.2140/pjm.1980.91.307

Abstract

A hyponormal operator is normal if it commutes with a contraction T of a Hilbert space, whose powers go to zero strongly, such that 1 − T^∗T has finite-dimensional range and the coefficients of the characteristic function of T lie in a commutative C^∗-algebra. The hyponormal operator is a constant multiple of the identity transformation if the rank of 1 −T^∗T is one.

Mathematical Subject Classification 2000

Primary: 47B20

Secondary: 47A56

Milestones

Received: 5 June 1979

Revised: 21 February 1980

Published: 1 December 1980