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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Bounded and compact vectorial Hankel operators


Author: Lavon B. Page
Journal: Trans. Amer. Math. Soc. 150 (1970), 529-539
MSC: Primary 47.40
MathSciNet review: 0273449
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Abstract: Operators $ H$ satisfying $ {S^ \ast }H = HS$ where $ S$ is a unilateral shift on Hilbert space are called Hankel operators. For a fixed shift $ S$ of arbitrary multiplicity the Banach spaces of bounded Hankel operators and of compact Hankel operators are described, and it is shown that the former is always the second dual of the latter. Representations for bounded and for compact Hankel operators are given in a standard function space model.


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DOI: https://doi.org/10.1090/S0002-9947-1970-0273449-3
Keywords: Bounded Hankel operator, compact Hankel operator, Toeplitz operator, shift, unitary dilation, trace-class, dual space, quotient space
Article copyright: © Copyright 1970 American Mathematical Society