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Lifting intertwining relations

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Abstract

This note is devoted to the lifting problem for the intertwining relation

$$XT_1^* = T_2 X,$$

where the T's are given contractions and X is a bounded operator. The lifting is possible if and only if X satisfies a stronger condition of boundedness introduced by the authors in a previous paper. The note includes a (partly expository) section which gives a simple proof of the commutant lifting theorem based on completing matrix contractions.

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Authors and Affiliations

  1. Institute of Mathematics, Czechoslovak Academy of Sciences Zitna 25, 115 67, Praha 1, Czechoslovakia

    Vlastimil Pták & Pavla Vrbová

Authors
  1. Vlastimil Pták
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  2. Pavla Vrbová
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Pták, V., Vrbová, P. Lifting intertwining relations. Integr equ oper theory 11, 128–147 (1988). https://doi.org/10.1007/BF01236657

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  • DOI: https://doi.org/10.1007/BF01236657

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