#### Title

The Absolute Continuity of Phase Operators

#### Document Type

Conference Proceeding

#### Publication Date

1975

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#### Abstract

Let H be a separable Hilbert space with orthonormal basis {φ_{n}}, V the unilateral shift operator on H so that Vφ_{n} = φ_{n+1}, and A be defined by Aφ_{n} = a_{n-1}φ_{n} with a_{0} = 0. Consider the operator C = 1/2(V*A + AV). If the sequence {a_{n}} converges monotonically to 1 and is so chosen that the spectrum of C is exactly the interval [-1,1], the operator C is called a phase operator. It was previously known that certain phase operators were absolutely continuous and that all phase operators had an absolutely continuous part. The present work completes the discussion by showing that all phase operators are absolutely continuous. (Received November 5, 1974.)

#### Repository Citation

Dombrowski, J.,
& Fricke, G. H.
(1975). The Absolute Continuity of Phase Operators. *Notices of the American Mathematical Society, 22* (1), A-193.

https://corescholar.libraries.wright.edu/math/256

## Comments

First published in

Notices of the American Mathematical Society22.1 (1975), published by the American Mathematical Society.