Bases in Banach Spaces II

Front Cover......Page 1
Title Page......Page 2
Copyright Information......Page 3
Preface......Page 4
Contents......Page 6
§ 0. Banach spaces which do not have the approximation property......Page 8
§ 1. Basic sequences. Bibasic systems......Page 54
§ 2. Deficient basic sequences. Images and inverse images of bases by continuous linear mappings......Page 110
§ 3. Complete sequences......Page 141
§ 4. Bases with respect to a class of sequences of indices......Page 148
§ 5. Pseudo-bases. Semi-bases......Page 157
§ 6. Minimal sequences. {λ_{i}}-linearly independent sequences. Complete minimal sequences. Maximal biorthogonal systems......Page 161
§ 7. Generalized bases......Page 196
§ 8. M-bases. Strong M-bases. Series summable M-bases......Page 226
§ 9. Approximative bases. Quasi-bases. Finite-dimensional expansions of the identity. Commuting approximative bases......Page 281
§ 10. Operational bases. Generalized summation bases......Page 332
§ 11. T-bases (summation bases). Strongly series summable M-bases. γ-bases......Page 356
§ 12. Π-bases. π-bases. π_1^{∞}-bases. The universal complements C_{p}......Page 413
§ 13. Dual π-bases. Commuting π-bases. Bases with parentheses. Finite-dimensional decompositions......Page 435
§ 14. Duality theorems. Further universal complement properties of the spaces C_{p}......Page 473
§ 15. Decompositions (bases of subspaces). Schauder decompositions. Resolutions of the identity. Integral bases......Page 491
§ 16. Bases of sets......Page 566
§ 17. ER-sets. Extended unconditional bases. Transfinite bases. Strongly unconditional integral bases......Page 578
§ 18. Extended approximative bases. Extended Π-bases. Extended resolutions of the identity......Page 610
§ 19. Transfinite decompositions. Transfinite Schauder decompositions. Ordinal resolutions of the identity......Page 628
§ 20. Extended biorthogonal systems. Extended M-bases......Page 680
Notes and Remarks......Page 724
Bibliography......Page 846
Appendix: Complements added in proof......Page 863
Bibliography to the Appendix......Page 874
Notation Index......Page 876
Author Index......Page 879
Subject Index......Page 882
Back Cover......Page 888