## Banach spaces which satisfy linear identities |

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### Contents

CHAPTER ONE BANACH SPACES AND UNIVERSAL LINEAR IDENTITIES | 10 |

CHAPTER TWO TWODIMENSIONAL SPACES IN | 32 |

CHAPTER THREE THREEDIMENSIONAL SPACES IN | 45 |

2 other sections not shown

### Common terms and phrases

2n root Amer argument ax+by Banach space beddable calculation Chapter coefficient compact complex constant convex function Corollary 44 counter-example defined degree 2n dimensional dyadic fraction elements embeddable in Lp equation Euclidean Spaces f u,v f(at+b,ct+d finite follows four-line lemma fourth powers Frechet function f g+xQh highest order term Hilbert space Hilbertian conditions holds identity Inner Product Spaces inner sum integral isometric Jordan-von Neumann Theorem k=0 K K Krivine leading term Lemma 27 Lemma 34 linear functions Lp spaces Math metric neighborhood norm function Normed Linear Spaces notation Orlicz spaces parallelogram law Parallelopiped Law perturbation polynomial of degree properties quadratic real two-dimensional space scalars second derivative Section space Xn subspace sufficiently small sum is taken Suppose Theorem 18 Theorem 20 three-dimensional space tion triangle inequality TT TT TT uniformly convex Uniformly Convex Spaces uniformly smooth vanishes variables verified x+ty x+ty|P xQh(s zero