iv CONTENT S 3.4. Basi c relation s betwee n H , H* , etc. 13 1 3.5. Th e "little " Grothendiec k inequalit y 13 2 3.6. Th e classe s o f a-integra l operator s betwee n Hilber t space s 14 2 Chapter 4 . Th e Fundamenta l Theore m an d it s consequence s 14 9 4.1. Function s o f type a 14 9 4.2. Th e Fundamenta l Theore m (Grothendieck' s inequality ) and it s variants 15 2 4.3. Consequence s t o th e theor y o f linear operator s 15 9 4.3.1. Composition s o f operators betwee n space s o f type C , L an d H 15 9 4.3.2. Linea r topologica l characterization s o f Hilbert spac e 16 0 4.3.3. A theorem o f Littlewood 16 1 4.4. A table o f the fourtee n natura l (g)-norm s 16 3 4.4.1. A summary wit h regard s t o th e characterization s an d factorizatio n schemes o f the variou s classe s o f integral operator s 16 4 4.4.2. Ther e ar e a t mos t 1 4 natural (g)-norm s 16 5 4.4.3. Ther e ar e exactl y 1 4 natural (g)-norm s 16 6 Notes an d remark s o n the complexificatio n o f tensor norm s 16 8 4.5. Note s an d remark s o n the natura l tenso r norm s an d Banach Algebra s 16 8 Further note s an d remark s 17 5 Glossary o f terms 17 7 Appendix A . Th e problem s o f the Resum e 18 3 A.l. Proble m 1 : Th e approximatio n proble m 18 3 A.2. Proble m 2 : Th e possibl e reductio n o f the tabl e of "natural " tenso r norm s 18 6 A.3. Proble m 3 : Grothendieck' s inequalit y an d th e "best " constan t 19 1 A.4. Proble m 4 : Algebraic-topologica l propertie s o f C*-algebra s 20 1 A.5. Proble m 5 : Characterizin g classe s o f spaces b y th e behavio r o f tensor product s an d th e actio n o f operators o n th e space s 20 8 A.6. Proble m 6 : Compariso n o f the projectiv e an d injective tenso r product s 20 9 Appendix B . Th e Blaschk e selectio n principl e an d compac t conve x set s i n finite dimensiona l Banac h space s 21 1 B.l. Blaschke' s Selectio n Principl e 21 1 B.2. Compac t set s i n Euclidea n space s 21 2 B.3. Ellipsoid s i n finite dimensiona l Banac h space s 21 6 Appendix C . A short introductio n t o Banac h lattice s 21 7 C.l. Th e facts , ma'm , jus t th e fact s 21 7 C.2. Som e basics abou t dualit y i n Banac h lattice s 21 8 C.3. Lattic e homomorphism s 22 2 C.4. AM-space s an d AL-space s 22 5 C.5. Kakutani' s vecto r lattic e versio n o f the Stone-Weierstras s theore m 22 7 C.6. Kakutani' s characterizatio n o f .AM-spaces wit h uni t 22 8 C.7. AL-spaces : Th e Freudenthal-Kakutan i theore m 22 9 C.8. Kakutani' s characterizatio n o f AL-spaces 23 4
Previous Page Next Page