CONTENTS Introduction.................................................................................................................................................. 5 Section 1. Notation basic fact and preliminary results....................................................................... 8 Section 2. Some results on Banach lattices......................................................................................... 12 Section 3. Ideals families of sets in a Banach space and Schwartz operator ideals................... 22 Section 4. Schwartz ideals determined by a Banach lattice.............................................................. 26 Section 5. Banach function lattices and the duality theorem of Schwartz..................................... 42 Section 6. Schwartz ideals determined by unconditional basic sequences in $L_p{0, 1)$........ 61 Section 7. Some concluding remarks and some open problems................................................... 68 References.................................................................................................................................................. 61
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