On the distance between unitary orbits of weighted shifts

Author:
Laurent Marcoux

Journal:
Trans. Amer. Math. Soc. **326** (1991), 585-612

MSC:
Primary 47B37; Secondary 47A30, 47C99

DOI:
https://doi.org/10.1090/S0002-9947-1991-1010887-9

MathSciNet review:
1010887

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Abstract: In this paper, we consider invertible bilateral weighted shift operators acting on a complex separable Hilbert space . They have the property that there exist a constant and an orthonormal basis for with respect to which a shift acts by and . The equivalence class of weighted shifts with weight sequence (with respect to the basis for identical to that of forms the *unitary orbit* of .

Given two shifts and , one can define a distance between the unitary orbits of and . We establish numerical estimates for upper and lower bounds on this distance which depend upon information drawn from finite dimensional restrictions of these operators.

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DOI:
https://doi.org/10.1090/S0002-9947-1991-1010887-9

Article copyright:
© Copyright 1991
American Mathematical Society