On the reduction of general Wiener–Hopf operators

  • Frank-Olme SpeckEmail author
Part of the Operator Theory: Advances and Applications book series (OT, volume 271)


The aim of this work is to present criteria for the equivalent reduction of general Wiener–Hopf operators \( W \,=\,P_{2}A|{P_{1} X}\, \text{where}\, X, Y\) are Banach spaces, \( P_{1}\,\in\,\mathcal{L}(X) , P_{2}\,\in\,\mathcal{L}(Y)\) are any projectors and \( A\,\in\,\mathcal{L}(X , Y)\) is a bounded linear operator, namely, to more special forms where X = Y and possibly P1 = P2 and/or A is invertible or even where A is a cross factor.

This is carried out with the help of operator relations: equivalence, equivalence after extension, matricial coupling and further related relations. Examples are given for the occurrence of different operator relations in applications.


Wiener–Hopf operator reduction operator relation equivalence cross factor generalized invertibility. 

Mathematics Subject Classification (2010)

Primary 47A68 Secondary 47B35 


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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Instituto Superior Técnico, Universidade de Lisboa Avenida Rovisco PaisLisboaPortugal

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