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A Short Proof of an Interpolation Theorem

Published online by Cambridge University Press:  20 November 2018

Edward Hughes
Edward Hughes*
Affiliation:
Carleton University, Ottawa, Ontario
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In this note we give a simple proof of an operator-interpolation theorem (Theorem 2) due originally to Donoghue [6], and Lions-Foias [7].

Let be the complex plane, the open upper half-plane, the real line, ℛ+ and ℛ- the non-negative and non-positive axes. Denote by the class of positive functions on which extend analytically to —ℛ-, and map into itself. Denote by ’ the class of functions φ such that φ(x1/2)2 is in .

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 17 , Issue 1 , 01 March 1974 , pp. 127 - 128
Copyright
Copyright © Canadian Mathematical Society 1974

References

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