BIORTHOGONAL SYSTEMS IN BANACH SPACES

By Z. RAIRI

CONTENTS SEPARABLE BANACH SPACES BASICS AUERBACH BASES EXISTENCE OF M-BASES IN SEPARABLE SPACES BOUNDED MINIMAL SYSTEMS STRONG M-BASES EXTENSIONS OF M-BASES ?-INDEPENDENCE EXERCISES UNIVERSALITY AND THE SZLENK INDEX TREES IN POLISH SPACES UNIVERSALITY FOR SEPARABLE SPACES UNIVERSALITY OF M-BASES SZLENK INDEX SZLENK INDEX APPLICATIONS TO UNIVERSALITY CLASSI?CATION OF C[0, ?] SPACES SZLENK INDEX AND RENORMINGS REVIEW OF WEAK TOPOLOGY AND RENORMINGS THE DUAL MACKEY TOPOLOGY SEQUENTIAL AGREEMENT OF TOPOLOGIES IN X? WEAK COMPACTNESS IN CA(?) AND L1(?) DECOMPOSITIONS OF NONSEPARABLE BANACH SPACES SOME RENORMING TECHNIQUES A QUANTITATIVE VERSION OF KREIN’S THEOREM BIORTHOGONAL SYSTEMS IN NONSEPARABLE SPACES LONG SCHAUDER BASES FUNDAMENTAL BIORTHOGONAL SYSTEMS UNCOUNTABLE BIORTHOGONAL SYSTEMS IN ZFC NONEXISTENCE OF UNCOUNTABLE BIORTHOGONAL SYSTEMS FUNDAMENTAL SYSTEMS UNDER MARTIN’S AXIOM UNCOUNTABLE AUERBACH BASES MARKUSHEVICH BASES EXISTENCE OF MARKUSHEVICH BASES M-BASES WITH ADDITIONAL PROPERTIES ?-SUBSETS OF COMPACT SPACES WLD BANACH SPACES AND PLICHKO SPACES C(K) SPACES THAT ARE WLD EXTENDING M-BASES FROM SUBSPACES QUASICOMPLEMENTS WEAK COMPACT GENERATING RE?EXIVE AND WCG ASPLUND SPACES RE?EXIVE GENERATED AND VA?S´AK SPACES HILBERT GENERATED SPACES STRONGLY RE?EXIVE AND SUPERRE?EXIVE GENERATED SPACES TRANS?NITE SEQUENCE SPACES DISJOINTIZATION OF MEASURES AND APPLICATIONS BANACH SPACES CONTAINING ?1(?) LONG UNCONDITIONAL BASES LONG SYMMETRIC BASES MORE APPLICATIONS BIORTHOGONAL SYSTEMS AND SUPPORT SETS KUNEN-SHELAH PROPERTIES IN BANACH SPACES NORM-ATTAINING OPERATORS MAZUR INTERSECTION PROPERTIES BANACH SPACES WITH ONLY TRIVIAL ISOMETRIES REFERENCES