With Pascual Jordan he wrote a short paper giving the first derivation of a given norm from an inner product by means of the parallelogram identity. His trace inequality is a key result of matrix theory used in matrix approximation problems. He also first presented the idea that the dual of a pre-norm is a norm in the first major paper discussing the theory of unitarily invariant norms and symmetric gauge functions (now known as symmetric absolute norms). This paper leads naturally to the study of symmetric operator ideals and is the beginning point for modern studies of symmetric operator spaces.
wItH Pascual jOrdAn hE WRotE a shorT pAPer giviNG the fIrst DerIvation oF a gIven nOrm FRom an innER Product By meanS oF The pArALlelOgraM IdEnTItY. His trace InequAlity is A keY REsULt OF matrIx ThEory used iN MATrIX APprOxImAtIon ProblEms. HE alsO first prEsented thE Idea That THe duAL of a Pre-norM Is a nOrm in the FIrsT major pAPEr dIScuSsiNg THe theorY of unItarIlY invAriANT NorMs and syMmEtrIc gauge funCtions (NOw known As sYmmetriC aBSoLuTE norms). This paPER lEADs naTUrALly tO the sTudy of syMmETric operaTor iDeaLs ANd Is tHe BeginnInG Point foR mOdERn StuDIes of symmEtric OPeratoR spacEs.