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2012 On compactness in‎ ‎complex interpolation
Jürgen Voigt
Ann. Funct. Anal. 3(1): 121-127 (2012). DOI: 10.15352/afa/1399900029


‎We show that‎, ‎in complex interpolation‎, ‎an operator function that is compact‎ ‎on one side of the interpolation scale will be compact for all proper‎ ‎interpolating‎ ‎spaces if the right hand side $(Y^0,Y^1)$ is reduced to a single space‎. ‎A corresponding result‎, ‎in restricted generality‎, ‎is shown if the left hand side‎ ‎$(X^0,X^1)$ is reduced to a single space‎. ‎These results are derived from the fact that a holomorphic operator valued‎ ‎function on an open subset of $\mathbb{C}$ which‎ ‎takes values in the compact operators on part of the boundary is in fact compact‎ ‎operator valued‎.


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Jürgen Voigt. "On compactness in‎ ‎complex interpolation." Ann. Funct. Anal. 3 (1) 121 - 127, 2012.


Published: 2012
First available in Project Euclid: 12 May 2014

zbMATH: 1271.46025
MathSciNet: MR2903273
Digital Object Identifier: 10.15352/afa/1399900029

Primary: 46B70
Secondary: 47B07

Keywords: ‎compact operator function , Complex interpolation

Rights: Copyright © 2012 Tusi Mathematical Research Group

Vol.3 • No. 1 • 2012
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